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