Answer
Answer Choice $G$
Work Step by Step
The easiest way to do this is by plugging in a point, and depending on if it worked with the inequalities given, you shade a side. Which ever side is shaded darker, that would be the answer. You could also use colored pencils. Plugin $(0,0)$ into the first inequality.
$0 \leq (-7)(0) + 12$
Since this is true, shade the side of $y = -7x+12$ that includes $(0,0)$
Do this for the second inequality.
$0 \leq -\frac{2}{3}$
This is false, so shade the side of $y = (-2/3)x-2/3$ that doesn't include $(0,0)$
You should get Region B as the darker area.
This would be the $G$
