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"Rule of thumb" density numbers you find online tend to be way too crowded for the Arizona heat. My birds are much happier if they have a lot more room. Especially in the heat of the summer. Assuming you have large fowl, you've got enough run space for 8-10 hens. But that coop is on the small side. Six birds would be okay in that coop. Maybe 8. It will depend on ventilation and shade. If the coop is elevated so they also have run space below the coop and you never close the coop so they always have access to outside, then you might get away with 10 birds in there. If you have bantams instead of large fowl, then 12 birds should be no problem.
Just remember that the more birds you put in there, the more manure they generate. The more manure generated, the more often you have to clean or add litter or otherwise maintain the coop. Even if you are using deep litter there will be maintenance. And given that your runs are under 5' in height, maintaining those runs is going to be a pain in the neck. Literally. So the fewer birds you have in there the happier the birds will be and the happier you are likely to be, because you won't have to be constantly adding litter or wetting down deep litter or raking things around or picking up chicken poop.