Well, this is not the easiest. With a bunch of unmarked white wires even seasoned people can easily get confused. You can look at useful references like
https://hid.venturelighting.com/TechCenter/BallastTypes.html for familiar wiring patterns.
By the way, that kind of question definitely deserves a better photo, where all the wires are visible and are spread out in a meaningful way as to be able to trace their origins!
From the picture, this is definitely an (auto)transformer ballast. For a small lamp, most likely just a leakage transformer (HX) or less likely, CWA circuit.
The coil with the most wires should be multi-tap primary. Sometimes, the connection to secondary is at 120V tap. In that case you can easily deduct this. Sometimes no, may be will require a creative play with an ohm-meter.
