You can't remove the airbox completely without actually dismantling it and even then, you have to remove the carbs first before you can get all the parts of the airbox out.
To remove the carbs, simply ensure that the airbox is as far back as it will go. To achieve this you need to pull the EXUP cables out to the right side of the frame and also move the coolant pipe that sits behind the airbox. Make sure also that the zip tie holding the rear tank support rubber doesn't have the locking block between the frame cross rail and the airbox.
With the above measures taken care of the airbox should pull back to give around 1cm clearance which is more than enough to get the carbs out. A squirt or two of WD40 helps ease things along.
Final tip. When you undo the rear clamps on the airbox-to-carb stubs, push them back on the stub and then tighten them up again. This stops them slipping forward and fouling when you slide the carbs out.
Or leave it for me to show you in December ...