Given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit can be repeated in an integer?

Since the digits can be repeated, you will simply have: 4^4 / 2^4 = 16 2-digit permutations as follows:

{2, 2} | {2, 4} | {2, 6} | {2, 7} | {4, 2} | {4, 4} | {4, 6} | {4, 7} | {6, 2} | {6, 4} | {6, 6} | {6, 7} | {7, 2} | {7, 4} | {7, 6} | {7, 7} (total: 16)