Answer
Graph "C" is the correct sketching.
Work Step by Step
For $y = |x| − 2,$
when $x=2, y=0, x=0, y=-2$ and $x=-2, y=0$
The curve passes through $(2,0), (0,-2)$ and $(-2,0)$.
Since the graph of $y=|x|-2$ is the same as the graph of $y=|x|$ but with a vertical translation of 2 units to the down, graph "C" is the correct sketching.