I have a Hunter Ceiling Fan Model # 21545 and I'm trying to install a Universal Fan and Light remote control with it. I'm having trouble with the wiring.

From the ceiling I have:
Green wire
Black wire
White Wire

From the fan I have:
Green
Black
White
Black/White

From the remote I have:
2 White
2 Black
1 Red

I'm uncertain as too which way the wiring is suppose to go, any help would be greatly appreciated.

I will not be able to finish this so maybe Ceilingfanrepair will jump in and help. The ceiling: green is ground, white is neutral and black is the hot (do not touch and kill the power) From the fan green still ground white is a common neutral to be shares for fan and light, black is not for motor and blk/wht is hot for the light. Here's wher I get stuck, you say remote but I think you mean the receiver that fits in the canopy. That has two sides and you only gave us one. The incoming side is going to be green/black and white, no brainer here. The outgoing side is normally black/white and blue so I am stumped for now. I'll drop a note to ceilingfanrepair and ask him to pay a visit.

The two black and two white should be marked differently from the remote, are they?

The receiver that fits into the canopy has 5 wires coming out of the same side.

2 black ( hot and fan)
2 white (common and neutral)
1 red (light)

I got the fan working fine, its just the remote control that's giving me trouble.

A guy at home depot told me to connect all the black and the red together and then all the white together. I did this but it still doesn't work. The ceiling fan and the light work. The only other thing I did was replace the dimmer switch on the wall that was used to control the old ceiling fan and replaced it with a single pole switch.

Ok common and neutral, one goes to the fan and one goes to the ceiling. Which one is paired up with the hot wire, and which one is paired up with the fan black?

Ceiling fan wiring - Ceiling Fans N More

Here is the solution:
Black / White (Remote) to Black / White (Ceiling)
Red to Black with White stripe of Fan (will power the lights)
Black to Solid Black of Fan (powers Fan)
White to White from Fan (Common)

That wiring is correct.

Ceiling Fan Wiring, Ceiling Fan Wiring Technical Help, Do it Yourself (DIY) - Ceiling Fans N More