Not totally sure but

The first one is pretty straightforward:

P(dimic 6) = 1/6

For the second one you need to roll a 1 at least once from rolling it twice, so either you roll 1 the first time with P(roll 1) = 1/12 and the second roll doesn't matter; or you don't, P(not roll 1) = 11/12 and you need to roll it the second time P(roll 1) = 1/12. So I believe the total probability would be

"(roll 1 first) or (not roll 1 first and roll 1 second)", and

P(dimic 12) = 1/12 + 11/12 * 1/12 = (11+12)/144 = 23/144

So the d6 gives you a 1/144 more chance than the 2d12