More often than not we do need to adequately help those that we need to help us by giving enough relevant information to go by with.
I agree that the problem given is impossible to solve especially when all the information given are so generalized and so lacking.
Even algebraic equations with various variables need more than just one related equation and values to solve all the unknowns.
It's really just like showing us an outside view of a wall with several wires sticking out of the surface and telling us that those wires are connected to an electric motor hidden behind that wall.
That motor has run and start capacitors that connects to at least two of the wires and that's all we have to go by with.
Nothing about the type, model , or make of motor and whether or not it has the capability to select the voltage ( 120 or 240V) for its power line input.
Now, we are asked to determine which among the unknown and unlabeled wires visible outside the wall are supposed to be connected to the various terminals on that hidden motor without any way of going behind that wall to inspect, test or perhaps trace connections to the motor windings when necessary.
I'm sorry if my frustration seems obvious.