Answer
Graph "H" is the correct sketching.
Work Step by Step
For $y = |x| + 2,$
when $x=2, y=4, x=0, y=2$ and $x=-2, y=4$
The curve passes through $(2,4), (0,2)$ and $(-2,4)$.
Since the graph of $y=|x|+2$ is the same as the graph of $y=|x|$ but with a vertical translation of 2 units up, graph "H" is the correct sketching.