Lets lay out these points in their appropriate quadrants.
(-5, 4) (5, 4)
(-5, -4) (5, -4)
If we look at the horizontal direction, the x coordinates in the boundaries are -4, -3, -2, -1, 0, 1, 2, 3, 4
If we look at the vertical direction, the y coordinate in the boundaries are -3, -2, -1, 0, 1, 2, 3
If you draw them out, you will see.
The horizontal has 9 x-coordinates. The vertical has 7 y-coordinates. These points form an array inside the rectangle. If we multiply 9 by 7, we get 63.
There are 63 integer coordinate points inside this rectangle.