You have the following equation:
4x + 3y = -24
the x-intercept is calculated by making y=0 and solving for x:
4x + 3*0 = -24
4x = -24
x = -24/4
x = -6
The x-intercept is (-6 , 0)
y-intercept is calculated by making x=0 and solving for y:
4*0 + 3y = -24
3y = -24
y = -24/3
y = -8
The y-intercept is (0 , -8)
When you placed the pervious points at the coordinate system and draw a line which crosses through those points, you obtain: