Question:

Was Luke there when Jesus was on the mount with Moses and Elijah? No! How did He know what to write?

Answer:
He was inspired of God as to what he wrote. “Every scripture is divinely inspired, and profitable for teaching, for conviction, for correction, for instruction in righteousness; that the man of God may be complete, fully fitted to every good work” (2 Timothy 3:16, 17, JND translation). “For prophecy was not ever uttered by the will of man, but holy men of God spake under the power of the Holy Spirit” (2 Peter 1:21, JND translation).

Luke 1:1-4 tells us that Luke heard from eyewitnesses what happened, “That thou mightest know the certainty of those things, wherein thou hast been instructed.”