I just moved to a new rental apartment and the refrigerator is making a very loud clicking noise. As a quick remedy, I thought I can clean the coils but I couldn't find them. I checked the back and under, but no luck. Maybe the pictures can give you an idea. Any help is appreciated..
I don't think cleaning the coils is going to solve the clicking noise, that is probably a more involved repair.
Since the coils are not in the compressor compartment shown in your photos (which would have been my first guess), the coils may be literally on the bottom of the refrigerator, usually accessible from the front panel at the bottom of the fridge. You can use a coil brush (like GE's PM14X51 brush) or perhaps a vacuum cleaner crevice attachment to clean them.
If you can't gain access to the coils from the front, it's possible that you'll need to tip the refrigerator over slightly to access them, but I haven't yet run into a case where that is necessary.
I can't quite make out the compressor tubing in your pictures, but you can probably follow that tubing to see where the condenser coils might be located.
If you have access to the fan, try to brush loose dust off the fan blades as well.
Make sure the refrigerator is unplugged when you clean the coils just in case you come into contact with the fan or live wiring
It's also possible that the coils are at the top of the refrigerator, but I've only seen that on built-in models, and they typically have an obvious vent or access panel to let you gain access to them.