I think this is it
1) there are 4 choices for the first row, the X can go anywhere. Just put your X in
2) There are only 2 choices for the next row because it cannot go in the same box as the first one did.
3) There are 2 choices for the next row because it can go in either box but it cannot go under either of the 2 x's that are already there.
4) There is only one possibility left for the last row
so the number of possibilities is 4*2*2*1=16