After you have the cable disconnected from the handlebar, I always remove the cables from the carbs, so you can get it out in the 'open' and work on it !
The trick to disassembling the splitter body is to screw the adjuster on the single cable from the handlebar all the way in, then unscrew the 'cap' to the splitter, you should have enough slack in the cable to get it out of it's 'detent' in the splitter block and then move the cable to the side, and then it should come right out.
You're going to have to hold the splitter block and the cable and push it in a little to get the cable dis-engaged.
Personally, your first time, I would remove the whole assembly from the bike, until you get the idea of how it works, it's simple but yet confounding at the same time !!!!
Hope this may have helped you out more than it confused you !!!