Is a 6x6 structure with 5'-6" high walls and the peak of the roof will be 2' from the top of the wall and a run that is 6'x12' big enough for 4 standards and 2 bantam chickens?
Yes and yes! If I was building a coop for that number/type of chickens, I would want a coop AT LEAST 20 sq. ft., and a run of AT LEAST 50 sq. feet. More room is ALWAYS welcome and beneficial, and you have that!!
I have 15 birds in an 8'x8' coop. They are only in the coop to roost and use the nest boxes. There is a feeder and waterer inside and outside their coop. They use the ouside feeder and waterer most.