I am replacing an exhaust fan/motor & a light with just a new exhaust fan/motor. I want to hardwire the new motor (2 black wires) to the house wiring (one each red, white, black, & ground wires).

I will assume you had 2 switches, one for fan and one for motor. Are you sure the motor has 2 black? Perhaps a white with black stripe? A motor needs a neutral and solid black is for power, not a neutral. This is most likely a shaded pole motor.

Are you saying that you want to replace a fan/light with a fan only unit?
Are you saying that you want to replace the fan motor only?
Are you saying that you want to wire the fan to run contentiously (not through a switch?)

Bath exhaust replacement motors usually come with a plug the fits in a receptical in the fan/light unit.

What brand and model fan are you working on? Most are not hard wired. The light and fan each have their own small plug which plugs into a junction box built onto the fan housing.

You need to trace the wires in the new unit because you are only running one 12 volt shaded pole motor which only needs a hot wire (usually black), a neutral (white), and a green ground wire to case. The red wire may be an extra wire or a wire for a two-speed motor where the red wire is low speed (cap this wire and never put power to black and red or it will instantly burn up the motor) and black is high speed. If you are using a new housing it may have a receptacle for the fan to plug into for power. The fan should be controlled by the wall switch. Use a volt meter and find out what the existing wires are wired to do. If you previously had a light and fan unit then you will have two hot wires, so only use one and cap the other one.