In the answer to an earlier question we looked at the units digit of 7 to the power 358. You can use the same method here. The technique is to consider 121, 122, 123 ..., watch the units digit in each case, and look for a pattern. If you also look at 21, 22, 23 ... you will se the same pattern. Since you are only interested in the units digit of powers of 12 you can solve this problem by only calculating powers of the units digit of 12.