The lesson is #13 “I Will Give unto Thee the Keys of the Kingdom” - and it's found in Mathew 17;
Mark 9;1 And after six days Jesus taketh Peter, James, and John his brother, and bringeth them up into an high mountain apart,
2 And was transfigured before them: and his face did shine as the sun, and his raiment was white as the light.
3 And, behold, there appeared unto them Moses and Elias talking with him.
4 Then answered Peter, and said unto Jesus, Lord, it is good for us to be here: if thou wilt, let us make here three tabernacles; one for thee, and one for Moses, and one for Elias.
5 While he yet spake, behold, a bright cloud overshadowed them: and behold a voice out of the cloud, which said, This is my beloved Son, in whom I am well pleased; hear ye him.
6 And when the disciples heard it, they fell on their face, and were sore afraid.
7 And Jesus came and touched them, and said, Arise, and be not afraid.
8 And when they had lifted up their eyes, they saw no man, save Jesus only.
9 And as they came down from the mountain, Jesus charged them, saying, Tell the vision to no man, until the Son of man be risen again from the dead.
10 And his disciples asked him, saying, Why then say the scribes that Elias must first come?
Luke 9;2 ¶And after six days Jesus taketh with him Peter, and James, and John, and leadeth them up into an high mountain apart by themselves: and he was transfigured before them.
3 And his raiment became shining, exceeding white as snow; so as no fuller on earth can white them.
4 And there appeared unto them Elias with Moses: and they were talking with Jesus.
5 And Peter answered and said to Jesus, Master, it is good for us to be here: and let us make three tabernacles; one for thee, and one for Moses, and one for Elias.
6 For he wist not what to say; for they were sore afraid.
7 And there was a cloud that overshadowed them: and a voice came out of the cloud, saying, This is my beloved Son: hear him.
8 And suddenly, when they had looked round about, they saw no man any more, save Jesus only with themselves.
9 And as they came down from the mountain, he charged them that they should tell no man what things they had seen, till the Son of man were risen from the dead.
10 And they kept that saying with themselves, questioning one with another what the rising from the dead should mean.
There are some great insights on this important event. Elder David B. Haight April General conference 1977 - "We Beheld His Glory"28 ¶And it came to pass about an eight days after these sayings, he took Peter and John and James, and went up into a mountain to pray.
29 And as he prayed, the fashion of his countenance was altered, and his raiment was white and glistering.
30 And, behold, there talked with him two men, which were Moses and Elias:
31 Who appeared in glory, and spake of his decease which he should accomplish at Jerusalem.
32 But Peter and they that were with him were heavy with sleep: and when they were awake, they saw his glory, and the two men that stood with him.
33 And it came to pass, as they departed from him, Peter said unto Jesus, Master, it is good for us to be here: and let us make three tabernacles; one for thee, and one for Moses, and one for Elias: not knowing what he said.
34 While he thus spake, there came a cloud, and overshadowed them: and they feared as they entered into the cloud.
35 And there came a voice out of the cloud, saying, This is my beloved Son: hear him.
36 And when the voice was past, Jesus was found alone. And they kept it close, and told no man in those days any of those things which they had seen.
https://www.lds.org/general-conference/ ... y?lang=eng
Another excellent article by Ray L. Huntington and Camille Fronk - Ensign January 1999 -Though difficult for us to understand, Jesus himself must have been strengthened and sustained by Moses and Elijah to prepare Him for the suffering and agony ahead for Him in working out the infinite and eternal atonement of all mankind. An angel from heaven would again in a few days strengthen Him when He would sweat great drops of blood in the Garden of Gethsemane.
The three chosen apostles were taught of His coming death and also His resurrection, teachings that would strengthen each of them in the eventful days ahead.
Testifying later, John said, “We beheld his glory, the glory as of the only begotten of the Father” (John 1:14); and the apostle Peter, speaking of this personal experience, wrote: “For we have not followed cunningly devised fables, when we made known unto you the power and coming of our Lord Jesus Christ, but were eyewitnesses of his majesty.
“For he received from God the Father honour and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased.
“And this voice which came from heaven we heard, when we were with him in the holy mount.” (2 Pet. 1:16–18.)
Peter, James, and John—they alone beheld the glory and majesty of the transfigured Jesus and undoubtedly received the keys of the kingdom. These three were yet to be taken to a spot in Gethsemane where they would behold his suffering as He took upon Himself the sins of the world that He might redeem us from the Fall and through His resurrection demonstrate to us that He is the Only Begotten of the Father in the flesh and show unto us that He is the Redeemer of the world.
These same three witnesses who were on the mount—Peter, the senior of Christ’s apostles, and James and John—appeared to Joseph Smith and Oliver Cowdery in 1829 and conferred upon them the Melchizedek Priesthood and gave to them the keys of the kingdom and apostleship.
Latter-day Clarity on Christ’s Life and Teachings - https://www.lds.org/ensign/1999/01/latt ... figuration
Bible Dictionary -The Transfiguration. The events of the Transfiguration as described in Matthew 17 [Matt. 17], Mark 9, and Luke 9 are puzzling without the insights provided by modern revelation. According to the text of Matthew, Jesus took Peter, James, and John to a high mountain where He was transfigured before the three Apostles. During the Transfiguration the Old Testament prophets Moses and Elijah appeared to the Savior and visited with Him. This event was also accompanied by the appearance of a bright cloud from which God’s voice was heard to declare that Jesus was His Beloved Son (see Matt. 17:1–9). From latter-day revelation we know more of what transpired on this holy mount. John the Baptist, as a spirit, was also in attendance on the mount (see JST footnote to Mark 9:4). Additionally, Peter, James, and John were privileged to see the future transfiguration of the earth in the millennial day (see D&C 63:20–21).
Transfiguration, Mount of
This very important event in the New Testament occurred about a week after the promise made to Peter that he would receive the keys of the kingdom of heaven (Matt. 16:13–19; 17:1–9). On the mount, the Savior, Moses, and Elias (Elijah) gave the promised keys of the priesthood to Peter, James, and John (HC 3:387), which enabled these brethren to carry forth the work of the kingdom on the earth after the departure of Jesus. These keys were later given to all of the Twelve.
The Transfiguration occurred in about October, some six months before the death of Jesus. The brethren saw the Lord in a glorified and transfigured state. They also saw a vision of the earth as it will appear in its future glorified condition (D&C 63:20–21; HC 1:283); saw and conversed with Moses and Elijah, two translated beings; and heard the voice of the Father bearing witness that Jesus is His beloved Son, in whom the Father is pleased, and commanding the brethren to hear (obey) Him. See also Mark 9:2–10; Luke 9:28–36; 2 Pet. 1:16–18.
The event is important in many ways: Necessary priesthood authority was conferred upon Peter, James, and John; the significance of the Savior’s work was emphasized; and the unity of various dispensations and the close relationship of Jesus and His prophets was demonstrated. Few events in the Bible equal it in importance. A similar event occurred on April 3, 1836, in the temple at Kirtland, Ohio, where the same heavenly messengers conferred priesthood keys upon the Prophet Joseph Smith and Oliver Cowdery (D&C 110).