So some assumptions on the details left out:
1. This is a single phase AC capacitor start 2 speed motor.
2. There is only one capacitor and it has only one cap value on it, with only 2 wires going to it.
3. It was previously working to start on either speed and no longer does.
4. You have a mechanical switch for changing the speeds, not mag contactors controlled by a switch.
The issue is, there are basically two ways of having a 2 speed single phase motor: there are two capacitance that are put in series for the low speed, in which case if one was bad, it would only work in high speed, or the main winding is split, so in low speed you only energized half of the winding, then all of it in high. So if it only starts in low, and half of the winding was bad, it wouldn’t run in high. So if it just will not START in high, but RUNS at high speed after starting in low, then the problem must reside in the speed selection system external to the motor.
But this brings up point 3 above. If it PREVIOUSLY worked to start in high and no longer does, then you need a wiring diagram to diagnose the problem. If it is new and you are WANTING it to start in high, the problem may be that it was never designed to do so. It’s very common to do that on 2 speed motors, especially those with a single capacitor and a split winding. That’s about point 4, because that is typically done via contactors and a timer. Starting in low is direct, but if you want to start in high, it goes through a timer that always starts in low and only allows switching to high AFTER the centrifugal switch takes the start cap out of the circuit.