Answer
$1 \le x \le 3$
Refer to the image below for the graph.
Work Step by Step
RECALL:
$|x| \le a \longrightarrow \color{blue}{-a \le x \le a}$
Use the rule above to obtain:
$-1 \le x-2 \le 1$
Add $2$ to each part of the inequality to obtain:
$\begin{array}{ccccc}
&-1+2&\le &x-2+2 &\le &1+2
\\&1 &\le &x &\le &3\end{array}$
To graph the inequality, plot the points at $1$ and $3$, then shade the region in between them.