The x-intercept of a function is the value of which y=0, or the coordinate points where the function crosses through the x-axis.
Observing the attached graph, you can see that the line crosses the x-axis at the point (8,0). This means that x=8 when y=0, which holds true algebraically since x+4y=8 -> 8+4(0)=8 -> 8+0=8 -> 8=8.
Therefore, the x-intercept of the function is x=8 or (8,0).