The opposite end of the diameter XY must be as far to the right of the y-axis as X is to the left, so the x coord of Y must be 4, because X is 4 units to the left (-4), and the centre of the circle is on the y-axis.
The y coord of Y is as far above y=4 as X is below y=4. X is 4-(-5)=9 units below y=4, so Y is 9 units above y=4, so y=13.
The coords of Y are (4,13), answer D.