A slope is a measurement of the angle of a line from the horizontal .
If two lines are parallel with each other it means that they have the same angle. If they have the same angle then their slope must also be the same.
Therefore the Slope of a Parallel lines are the same.
So for our question if the green line and the red line are parallel they must have the same slope. And since the slope of the green line is -4 the slope of the red line is also just -4.