What do you call the that black box on inside of passenger side fender operates all front headlights a 1996 q45?

The black box you're describing in the passenger side fender of a 1996 Infiniti Q45 is most likely the Headlamp Control Unit (HCU). It's responsible for controlling the front headlights, including their brightness, high beam operation, and other functions.

It's also possible that the black box you're referring to is a relay for the headlights. Relays are electronic switches that are used to control the flow of electricity to the headlights.

To be sure, you can:

1. Locate the HCU: Refer to your 1996 Q45's owner's manual or an online repair manual for the exact location of the HCU. It's typically near the headlights.

2. Look for markings: The HCU or the relay may have markings on them that identify their function.

If you're still unsure, you can consult with a mechanic or an automotive electrician who can help you identify the specific part.