Don't worry, you're not the only one who had to endure this pain...
I had an old KZ650 I pulled the carbs from what it looks like a similar design. Like yours, it was older and the plastic air intake tubes were very stiff. Here is what I had to do.
- Pull gas tank off and disconnect from carbs.
- Pull the seat off to access the air filter and air box.
- Pull out the air filter and you will see the 4 intake tubes to the carbs.
- The air tubes to each carb are suppose to be pulled back into to the air box. This is very difficult to do when the plastic is so dried out and stiff. I used lots of WD-40 and tools to wedge them out. There are a few websites out there where you can order new tubes if you end up destroying the air tubes.
- Once you pull those air tubes back, you can loosen up the front side of the carbs from the intake and pull the entire carb assembly back and out. You will also need to disconnect the throttle and possible one or two bolts.
I then cleaned out every carb and put it back together. Sliding those individual air tubes back forward and into place took a lot of work and the help of a friend. I got it back together, but I really damaged and scratched up the air tubes from the air box. It worked great though, just looked bad.