I removed the throttle cable from the carbs once... I won't do it again though. I thought it would make it easy, but getting that bitch back in/on there was more trouble than it was worth damnit
You need to get into the assembly at the side of the carb to detach this. Honestly, might be easier to disconnect the OTHER end of the cable, and just let that long thing hang on there while you work with the carbs ? Like I said, I did it at the carb once, and won't do it again...
I would definately take a look at the jets to be sure they aren't clogged. Check the pilot jets too, not just the mains. Use some good carb or even brake cleaner in pinch and make sure they're totally clear.
Yes, the bowls are on the bottom of the carb. Inside each of the bowls there is a plastic 'float'. Each of those floats has a tiny metal spring (or 'tang') holding the float into position at the pivot point. These can easily bend out of whack and not allow the fuel to flow properly. Mine got bent over the winter without being ridden since it was running great- go figure ... it happens. Take a look at this if you're not getting gas into the carbs.
When my tang was bent ( LOL... I love sayin that) , I was getting gas to the right carb just fine, while the left was bone dry. I could force it to start and run by 'choking' the carbs with my hand, and could tell I was getting gas to the right carb, but even choking it out, my left carb was still dry. In the end it was that tiny-ass little tang keeping the float locked into place.
Moral of the story: If you wanna ride, be sure to take care of your tang ! LMFAO...