N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 2. What is the remainder when N is divided by 12?

By Chinese Remainder Theorem, there exists exactly one unique residue\(\pmod{12}\) that satisfies the given conditions. In this case, it is not difficult to notice that a residue of \(\boxed{2}\) works.