ROY - D&C 58:42 says when the Lord forgives you he no longer remembers it. I seem to remember that one of the Prophets said that he remembered it"Against" you no more. Memembers of our HP class said that he simplely forgot the sin. Please help.

JOEL - D&C 58:42 says:
"Behold, he who has repented of his sins, the same is forgiven, and I, the Lord, remember them no more."

This promise is also found in Jeremiah:
"For I will forgive their iniquity, and I will remember their sin no more." (Jer. 31:34.)

Is it possible for God to literally forget something? It would seem to contradict His omnipotent and/or omniscient character. But then again perhaps because He is omnipotent He has a way of completely removing it from His mind, so it is as if it never existed in the first place. I don't know. Some have suggested that the language used in such scriptures is meant to be understood metaphorically; that it is another way of saying that if we repent God will no longer hold us liable for the sin.

Your memory is correct. President Gordon B. Hnckley did say the following:
"Eternal vigilance is the price of eternal development. Occasionally we may stumble. I thank the Lord for the great principle of repentance and forgiveness. When we drop the ball, when we make a mistake, there is held out to us the word of the Lord that he will forgive our sins and remember them no more against us. But somehow we are prone to remember them against ourselves." ("Don't Drop the Ball," Ensign, November 1994, p. 48.)

So perhaps God does not literally forget the sin, the same as a mortal might forget something, but He is able to either willfully block it out of His mind or at least He will not use it against us come judgment day. Whatever it means, the results are the same; our repented sins will not impede our salvation.