This would be a permutation question.

We have 4 choices, 0, 3, 7, 8

As we wish to make a 4-digit number abcd.

For d, the units, we have 2 choices, 3 or 7.

And for each of the other digits, a,b,c we have 4 choices, 0,3,7,8.

Hence the our total number of choices are 4x4x4x2