Answer: D

Small Hint:

For $x<0$, $|x|=-x$

Big Hint:

Evaluate the absolute values from the inside outward

Solution:

Since $x=-2016<0,$ we have $|x|=2016.$ Thus $$\begin{aligned} |x|-x&=2016-(-2016) \\ &=4032, \end{aligned}$$ so the innermost absolute value is $4032.$ Therefore the full expression is $$|4032-2016|+2016=4032.$$

Thus, the correct answer is D .