CC12 Contactor is Confusing
First a few clarifications, the contactor you posted is the CC12SA120, the A120 in that part number indicates a coil operated by 120VAC. So if this particular contactor pictured has a 24VDC coil, then the part should be the CC12SD24.

If you have 24VDC control and the contactor you are trying to connect is the 120VAC coil version then you would have to find a way to change your control voltage (not commenting on because I do not know your control setup), or purchase the correct contactor.

This contactor allows for a 3-phase connection but because of your reply in comment that this application is a single-phase 120VAC motor, you only need to use one set of terminals. I would suggest connecting your supply to L1 and the motor to T1.