I read the coop as (8x12)-(8x4), so 64 sq ft. If I'm wrong and it's (8x12)+(8x4) then yes you have 96 sq ft plus an additional 32 sq ft (which doesn't count as coop space) which would house up to 24 or so birds. It sounds like I read it wrong!
I actually feel 10 sq ft per bird is too small...
General numbers for recommended minimums:
4 sq ft per bird in coop
10 sq ft per bird in run
1 linear ft per bird on roost (so plan on putting in that 3rd roost)
1 nest box per 3-4 hens
Note these are general guidelines, however you will find more space is never an issue, while too little space...