#### Answer

$(\frac{16}{3}, +\infty)$
Refer to the image below for the graph.

#### Work Step by Step

Solving the inequality will be easier of there are no fractions involved.
To get rid of the denominators, multiply the LCD of $6$ on both sides of the inequality to obtain:
$6(\frac{1}{2}x-\frac{2}{3}) \gt 2(6)
\\\frac{6}{2}x-\frac{12}{3|} \gt 12
\\3x - 4 \gt 12$
Add $4$ on both side of the inequality to obtain:
$3x \gt 16$
Divide $3$ on both sides to obtain:
$x \gt \dfrac{16}{3}$
The solution set includes all real numbers greater than $\dfrac{16}{3}$.
In interval notation, the solution set is:
$(\frac{16}{3}, +\infty)$
To graph the solution set, plot a hole (or hollow dot) at $x=\frac{16}{3}$ then shade the region to its right.
(refer to the attached image in the answer portion above)