How do I do this? What is the probability of rolling a die twice and rolling a 6 the first time and an even number the second time? Is it 1/12, 4/32, 5/32, or Not Given?

The prob of rolling a 6 is 1/6

half are even, half are odd faces so the prob of an even number is 1/2
so prob of the event you stated is 1/6*1/2
=1/12