Question

Explain why (–4x)0 = 1, but –4x0 = –4.

Answer 1

... what you have there does not make sense.

Answer 2

(Assuming that you mean (-4x)^0=1 and -4.x^0=-4)
(-4x)^0=(-4)^0 . x^0=1.1=1 and (-4) . x^0=(-4).1=-4.