What digit appears in the units place in the number obtained when 2^320 is multiplied out?

Let's start with 2^x and see if we can find a recurring pattern to help us find the answer

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = (1)6
2^5 = (3)2
2^6 = (6)4 
2^7 = (12)8
2^8 = (25)6

If you notice, the pattern is 2,4,8,6 in the units place. Every four consecutive x's, the cycle repeats. So at 2^4, 2^8, 2^12 (4096), and 2^16(65336), the units place will all be 6, since x is always divisible by 4 here. When x= 320, we know that 320 is divisible by 4. This means that for 2^320, the units place will also be 6.

Hope this helps, even though it's rather vague!