When you told my cousin he needed a heavier gauge wire than normal, I can only assume you knew why.
His system is overkill. 1600watts RMS. This cannot possibly make a nice, balanced sound, but that's my personal opinion. Your customer gave you the specs of their hardware (a premium brand amplifier pushing a verified 1650 watts rms, 3400+ peak on its 'birth sheet') and trusted your recommendations. They paid you a premium, because you have a good reputation in his town. You don't need to exercise much judgment here. Just figure out about how many feet of wire, look up the amps/watts conversion (protip: divide watts by 10 on a car to get a nice, round number with some safety built in, or 12 if you are cheap) and check your wiring chart.. Instead, you chose to install the wire on the left, and proceed to tell him it was 0 gauge. The wire on the right is from my own stash I use for wiring up my 48V solar panel battery banks/car projects. It's very chunky, hard to work with, but is only 2 gauge. After stripping back your so-called 0 gauge wire and mic'ing it, it is only 8 gauge. You lying bastard.
I knew as soon as I saw its melted husk you had not done this properly. I will give you credit, the ring terminals are not badly installed. It took me TWO tugs to pull it off. You could have burned his car down, along with him. The wire was routed properly, though apparently you think that grommets are for PUSSIES. When you punch through the firewall, please install a grommet. You mounted the fuse to the fender, good work!. You used screw on compression fittings when you clearly have some sort of terminal crimp, (which you either don't know how to use or its crap) so you lose points there. You installed a cheap fuse holder, but quite frankly that's not a big deal. What i also take issue with is how you tapped the battery. Just because its a side post does not mean you can simply unbolt it and stick your terminal between the battery and the cars positive and call it good. Use the proper fucking setup next time. Moron. Please Google 'big 3 upgrade' so you know how to upgrade a fucking ground, alt, and engine -> chassis ground please.
All said, my cousin is out 600 bucks for your shitty install. No permanent damage, and tomorrow him and I will do this right. I will bag your shitty melted wire and he can give it back to you when he does a chargeback.