You can't "solve" the equation because it involves two variables and there's only one equation. But the equation establishes a relationship between x and y which can be plotted as a graph. The graph is a straight line, and all you need is two points to join together. The graph will pass through both points.
The easiest way to do this to find the intercepts. Put x=0, and we get 4y≤8, so y≤2. Now put y=0, and we get 0≤x+8 so x≥-8. For the minute, forget the inequality and treat it as equality. We have two points (0,2) and (-8,0). Draw a line through these points. This is the line 4y=x+8.
Now consider the inequality. All points on the line are included. So what does 4y≤x+8 mean? It means y≤x/4 + 2. That's the area under the line because y is the vertical axis so the inequality means all values of y up to, but not beyond, y=x/4 + 2, in other words, lower than or on the line.