8 X atoms present at the corners.

Atoms contribute to 1 unit cell $$ = {1 \over 8} \times 8 = 1$$

6 X atoms present at the face centres.

Atoms contribute to 1 unit cell $$ = 6 \times {1 \over 2} = 3$$

Total X atoms $$ = 3 + 1 = 4$$

4 M atoms present at edge centres.

Atoms present in 1 unit cell $$ = 4 \times {1 \over 4} = 1$$

1 M atom present at body centre and it contribute completely to 1 unit cell.

Thus, total M atoms in one unit cell $$ = 1 + 1 = 2$$

Ratio is $$M:X::2:4::1:2$$

Thus, empirical formula is $$M{X_2}$$.