Half of the floors have different numbers of apartments. Half the number of floors is 12 floors / 2 = <<12/2=6>>6 floors.
One half of the block consists of 6 floors * 6 apartments/floor = <<6*6=36>>36 apartments.
And the other half consists of 6 floors * 5 apartments/floor = <<6*5=30>>30 apartments.
There are 30 + 36 = <<30+36=66>>66 apartments on all floors in the block.
All the apartments can therefore accommodate 66 apartments * 4 residents/apartment = <<66*4=264>>264 residents.
#### 264