The graph of the system of inequalities is in the image at the end.
How to solve the system?
We have the system of inequalities:
4x - 2y < 8
-3x - 2y > 6
First, let's isolate y in both cases, we will get:
1) 4x - 2y < 8
4x - 8 < 2y
(4x - 8)/2 < y
2x - 4 < y
2) -3x - 2y > 6
-3x - 6 > 2y
(-3x - 6)/2 > y
-1.5x - 3 > y
Then the system is:
y < -1.5x - 3
y > 2x - 4
To graph the system just graph the two lines as dashed lines (this is because the points in the lines aren't solutions)
Then:
For y < -1.5x - 3 shade the region below the line.
For y > 2x - 4 shade the region above the line.
The solution set of the system of inequalities is the intersection between the two shaded areas: