To the OP
The reason they are asking about your set up is because it takes a considerable amount of juice to run even the most efficient mini fridge pulling 6.4a when the compressor is running. Others use twice that.
The next questions will be for how long and how will you replace the power you use running the fridge. You need to have it all balanced out or risk running out of power or damaging the batteries.
One thing to consider here would be a 12v compressor fridge. They are more expensive but you spend more money on the fridge, not the batteries and solar/ generator and the space they take up. You will still need battery and some means of recharging, just not as much.
It's a trade off one way or another. I have the bank and solar to run the cheap fridge and more, it wasn't cheap, small or light. Also remember the batteries power more than just the fridge too.