At 2 Peter 3:10 we are told: “the heavens will pass away with a great noise, and the elements will melt with fervent heat; both the earth and the works that are in it will be burned up.” There are multiple things going on in 2 Peter 2:10, so let us take Genesis 8:21 first. There God was saying that he would never destroy the world in the same way again, in other words, by means of floodwaters. 2 Peter 3:10 is talking about fire, a whole other means.
According to 2 Peter 3:10 in the King James Version, “the earth also and the works that are therein shall be burned up.” However, other modern translations read, “the earth and the works that are done on it will be exposed [or discovered].” This comes about because there is a textual problem, The Codex Sinaiticus and Vatican MS 1209, both of the 4th century C.E., and other manuscripts, read (huerethesetai) “be discovered.” Later manuscripts, the 5th-century Codex Alexandrinus and the 16th-century Clementine recension of the Vulgate, read (katakaesetai) “be burned up.”
Now looking to the context in 2 Peter, are we talking about the literal earth anyway. Verses 5 and 6 speak of the flood in Noah’s day, likening it to “the day of judgment and destruction of the ungodly” (3:7). First, what was destroyed by the floodwaters? It was not the earth itself that was to be destroyed; it was ungodly men. This is exactly what Peter is talking about as well. The planet earth is not going to be destroyed on judgment day, it will be ungodly men. What is to be “discovered” on the earth in those days after the judgment is righteousness.