I am replacing my condenser fan motor the new motor wiring is different from the old (failed) motor. I got the L1 L2. My question is about the capacitor. I have a brown and a brown/white. My question is do I just hook those 2 wires brown and brown/white to each side of the new capacitor? Is the only wires going to the capacitor the brown and brown/white and nothing else.

The brown & brown/white go to the capacitor. The other two, it's had to say without a wiring diagram. With a heat pump, the condenser fan shuts down when the unit goes into defrost mode. If you connect those two wires to the contactor, the fan will not shut off in defrost.

L1 to the defrost board and L2 to the contactor. Just wasn't sure about the capacitor, just making sure no other wires needed to land on it besides brown and brown/white. This is correct right?

L1 to the defrost board and L2 to the contactor. Just wasnt sure about the capacitor, just making sure no other wires needed to land on it besides brown and brown/white. This is correct right?

Sounds like you've got it.