Well, here is the physics/math answer to your question:
Group 27s whether FLA or AGMs typically store 75 AHs of power each. So 6*75= 450 AHs. But discharging below 50% reduces battery life so you should not use more than 225 AHs. 225*12= 2,700 watt hours available in that case.
Your friend has a 12,000 BTU/hr A/C system as I recall. These typically draw 12 amps or 120*12= 2,440 watts. If run continuously and you will if you are just cooling down, then you can power your A/C for about an hour.
Then it will take at least 2,700 watt hours to recharge those batteries fully for the next time. Solar panels generally can produce 4 times their wattage rating in watt hours for a sunny day. So it will take about 700 watts of panels to recharge them.
If you want to run the A/C all night which will probably be at 50% duty cycle then it will take about 4-5 times the battery capacity and 4-5 times the solar panel wattage to do that.
David