How to determine what ballast for fluorescent lights?
You have a 15 watt T8 lamp and a ballast for four 32watt T8 lamps. No, it is not the right ballast. The info is in the ballast part number and the description of it in your Amazon link. Just google: 15 watt T8 ballast for the correct one. I came up with Keystone CC579TP or CC 1322TP or Magnetek 200-H2.  I am sure there are many others. Make sure that the one you pick has one  F15T8 in the list of applical bulbs and it does not require a starter.. The first one I listed showed a wiring diagram. The ballast has 2 leads and the bulb has 2 pins on each end. One ballast lead goes to AC, the other goes to a pin on one end of bulb the other pin on that end goes to a pin on the other end of the bulb. The last pin goes to AC. Of course, you probably want to include a power switch.