Answer
$(\frac{16}{3}, +\infty)$
Refer to the attached image below for the graph.
Work Step by Step
For easier work, get rid of the fractions by multiplying the LCD of 6 to both sides to have:
$\\6(\frac{1}{2}x - \frac{2}{3}) \gt 2(6)
\\3x - 4 \gt 12
\\3x \gt 12+4
\\3x \gt 16$
Divide 4 to both sides to have:
$\\x \gt \frac{16}{3}$
