I have a 5 KW genset that puts out 42 amps. I run a 16000 BTU reverse cycle air conditioner/heater and it only uses about 16 amps.
A 6 KW generator should be putting out close to 50 amps so you could run several units.
Generators like being run at about 75-80% of max. Don't oversize the generator. I also run other appliances to get the amps used up over 30.