My honda cbr 600 wont start and keeps backfireing

Check your plugs. If all four are sparking then your carbs are out of sync. They will need to be re-balanced.

If you are capabable in doing this job your self, you will need a screwdriver that fits your adjuster screws and a CarbTune Carb balancer.
Remove your tank and airbox.
You should see the flaps inside your carbs. These should open when you move your throttle.
Start on the outside carbs to get them balanced with the 2 centre ones.
To start, unscrew the adjusters all the way out. then screw them in until the 2 outer carbs move at the same time as the inner 2 carbs
Once this is done then adjust the centre balancer to syncronise the 2 left hand carbs to the 2 right hand carbs.
Now if you have done this correctly, all four carbs should open at the exact same time.
If you have a Carbtune balancer, remove the plugs from the top of your inlet manifold and plug in the hoses from the carbtune balancer.
Start the engine and adjust the screws until the weights inside the Carbtune balancer all read the same.
Once done, remove the balancer, replace the plugs into the inlet manifold, refit the airbox and tank and it should run so much better.

If your not 100% confident to unertake this job yourself, take the bike to your local dealer and ask to have the carbs balanced.