U means union, which means cases X OR Y is satisfied.

In your example, it means the first die is 6 or the sum of the dice is 10.

So X U Y will be (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) (4, 6) (5, 5)

There are 8 cases. So N (X U Y) is 8.

inverted U means intersection, which means cases X AND Y are satisfied.

In your example, it means that the first die is 6 and the sum of the dice is 10.

So X intersect Y will be only (6, 4)

There is only 1 case. So N (X intersect Y) is 1.

Hope this helps.