I have two cables running to exhaust fan hook up, each cable with one white and one black. Do I need both black and both white from the cables with the one black and one white from the new exhaust fan? Then what do I do with the green ground wire?
Chances are one cable is the source, and the other is a switch loop. You'd need to safely test to be sure, though. If that's the case, here's what it should look like:
If you don't have a grounding conductor (bare wire) in your cable, ignore the ground wire in your fan kit. There's not much you can do about it without running new wire. It's probably a low-risk issue anyway.
Sorry your question slipped through the cracks. I hope you got it resolved.
Does you old exhaust fan have a light also? Why do you have two sets of wiring for one exhaust fan? You could turn on the exhaust fan switch on the wall and check the voltage of the two sets of wires. Which ever set of wires has 110-120 volts, then use that set of wires to tie into the new exhaust fan. Wire nut and tape the other set of wires.