We have one in our current unit. Draws about 50w when operating, so worst case is 1200w-hr per day but assuming you don't camp in Arizona in the summer, 50% duty cycle would be more typical, so about 600w-hr/day.
A 50w solar panel will generate around 200-250w-hr/day.
So over 4 days,
- The solar panel would provide about 800-1000w-hr.
- The fridge would consume around 2400w-hr.
Therefore the battery bank would need around 1600w-hr of usable power or about 135amp-hr @ 12v. Of course, you can't use 100% of any battery bank, so:
- Lead Acid, you need about 270amp-hr (50% usable)
- Lithium, you need about 170amp-hr (80% usable)
I'm guessing from the description, he doesn't have a significantly upgraded battery bank, so unlikely he will be able to go 4 days without generator/shore power to supplement.
Bump up to 150-200w total of solar panels and it's probably viable but some of the above are estimates that will vary from day to day and how you use it (a teenage kid staring into the open fridge door regularly will up the usage)
PS: This ignores any other power draws. If you are running a lot of lights, an inverter or other items that consume a lot of w-hr, you will need additional upgrading to meet the loads.