These problems are fairly easy to work if you do what the instructions and hints tell you to do.
Quadrilateral WXZS is a rectangle of length 42 and width 11. Thus segment SY is 19-11 = 8 units, and WSY is a right triangle. By the Pythagorean theorem,
WY² = WS² +SY²
WY² = 42² +8² = 1764 +64 = 1828
WY = √1828 ≈ 42.76
The distance between the centers of the two circles is about 42.76.