You have a triangle with one side with length of 5 (from point 4,-4 to a point on the x-axis) and another side with length of 4 (from point 4,0 to point 4,-4). The third side of the triangle is obviously 3, because of Pythagoras rule. And that third point is on the x axis and 3 units away from point 4,0. So the third point can either be 1,0 or 7,0. Those two points are the answers.
