One of the most common mistakes made when installing 12V Compressor Fridges is to read the consumption figures and size the cable based on that.
6mm is really the minimum size and sometimes 10mm is the cable run is fairly long.
Reason why you need the thicker cable is to avoid the voltage drop on the inrush when the compressor kicks on - that will draw a current way higher than the numbers quoted in the manual. And if the cable is too thin, the voltage drop will be so great the fridge will see a "Low Battery" situation and not start, even though the battery itself could well be perfectly fine.
This is an example of the inrush power for my setup when the Fridge kicks on...
Fridge pulls 74W from the system (Fridge+Inverter) when running, but that momentary inrush is way higher as you can see.