Most likely flooding due to the float valve seat O rings in the carb/s leaking, the float bowls are filling up and and the overflowing petrol is running into the cylinders Common problem on the Fazers as they get older.
Only option is to remove the carbs and change the O rings. Easy enough job with the hardest part being removing and replacing the carbs. As the carbs are off and open do the main Jet O Ring also
Viton® (FKM) O-Rings are probably best and use seal type Fkm 75 or 80
O Ring sizes are :
Float needle valve: 7.5mm ID x 1.5mm cross section x 10.5mm OD
Main Jet : 5.5mm ID x 1.5mm cross section x 8.5mm OD
These can be bought locally in a Seal suppliersr bearing suppliers and Yamaha do not supply these O Rings
You may have to change the float seal, if so sometimes Suzuki ones are usually cheaper and part number which fits the Fazer 1000 and Fazer 600 is 13258-04F00
The advantage of changing just the O rings is that you don't have to reset the float heights after since you are refitting the same Needle Valve seat.