4x + y =8
The two intercepts are obtained by putting x=0 and solving for y,
and by putting y=0 and solving for x. Doing this we get that the
two intercepts are (0,8) and (2,0). The boundary line is the line going
through these two points.
Now it seems to me that the test point (-2,-3) is to the left and below
the line through (0,8) and (2,0), and as:
4(-2) - 3 < 8
this point is in the region that satisfies the inequality, so you should
shade the region to the left of the line.