We have to find integer values of x for which -4x > 16 (why only integer values because it is given that x ∈ Z that is set of integers)

-4x > 16

⇒ -x > 4

⇒ x < -4

The integers less than -4 are -5, -6, -7, -8, …

Generalizing the solution in terms of n

x = -(4 + n) where n is integers from 1 to infinity

Hence solution of -4x > 16 is x = -(4 + n) ∀ n = {1, 2, 3, 4…}