Number of matrices , such that sum in each row and each column is 0

To find number of 4 cross 4 matrices, such that each element is 1 or -1. Also sum of elements in each row and each column should be zero.

I am able to think that each row and each column shall consist of two 1 and two -1. But then how to proceed further

Hint: across any row and down any column, your choice in the first three elements uniquely determines the fourth. As such, you can consider the number of $$3 \times 3$$ matrices with entries in $$\{1,-1\}$$ such that no row/column $$\mathbf v$$ has $$v_1 = v_2 = v_3$$ i.e. all entries are the same.