Answer
$x\gt 6$
Refer to the image below for the graph.
Work Step by Step
Multiply $2$ on both sides of the inequality to obtain:
$2 \cdot \frac{1}{2}x \gt 3 \cdot 2
\\x \gt 6$
To graph this inequality, plot a hole (or hollow dot) at $x=6$, then shade the region to the right of $6$.
(refer to the attached image in the answer part for the graph)