Check the picture below.
now, we can solve x + 2y ⩽ 8, to what you see there in the picture, and as you already know, we start off by graphing the linear-version of it, namely x + 2y = 8 and the line of 3x = y, then after that we do the shading.
the lines are solid, because is ⩾⩽ and that includes the points along the line, for the shading we check the regions for "true" or "false" values, and the solution is where both shades meet, namely the "purple" area.