-(x+4) ≤ y ≤ (x-5) (I assume this is what you meant)
I'll do the first one.
Plug in (x=-5,y=2)
-(-5+4) ≤ 2 ≤ (-5-5)
1 ≤ 2 ≤ -10
1 is less than or equal to 2, but 2 is not less than or equal to -10. So (-5,2) is not a solution.
Do the other points the same way.
You graph the two inequalities on a coordinate plane. Each inequality requires shading on one side of the line. Once you have the shading in place, you graph the four points. The points which are in the region shaded by both of the inequalities are solutions.