http://www.ninjette.org/forums/showthread.php?t=70526
Slick explained his process to me at the bottom
The airbox is held in place by 2 bolts (top right towards the rear, bottom left towards the front). You should be able to move it back at least an inch after removing the battery.
These are my steps to removing the carbs:
1. Remove battery and its holder.
2. Remove both bolts holding down the airbox.
3. Loosen all clamps on the engine boots.
4. Pull airbox back as far as you can so carbs clear the boots.
5. Remove engine boots.
6. Loosen airbox boots.
7. Slide carbs forward to clear boots.
8. Slide carbs through the left side. (Bracket for idle adjuster must be removed)
Putting them back in is exactly in reverse.
I had an issue where my air box wouldn't moved, confirmed by another member, and we eventually got it to break free and wiggle back