In this problem, f(-x)=|-x+4|-|-x-4|

Because it is an absolute value |-z|=|z|.

So |-x+4|=|x-4| |-x-4|=|x+4|

So f (-x) = |-x+4 |-x-4 | = | x-4 |-x+4 | =-f (x)