Answer
Graph "G" is the correct sketching.
Work Step by Step
For $y = -|x|,$
when $x=2, y=-2, x=0, y=0$ and $x=-2, y=-2$
The curve passes through $(2,-2), (0,0)$ and $(-2,-2)$.
Since the graph of $y=-|x|$ is the same as the graph of $y=|x|$ reflected across the x-axis, graph "G" is the correct sketching.