Start by graphing each line as if it contained an equal sign.

x + 2y 8  →  y = (-1/2)x +4

y x + 4  →  y = x + 4

  Each of these graphs will have SOLID lines because of the less than or equal to conditions.

The test point chosen here for both shadings was (0,0).  This test point made both inequalities true, so the shading from each line covered the test point.

The solution, S, is the area where the two shadings overlap.