marcus and joannie are having a new family room added on. The length of the room is 6 feet less than double the length. If the perimeter is 78 feet,what is the dimension of the room?

I assume you mean the length of the room is 6 feet less than double the WIDTH.

L = 2W - 6

P = 2L + 2W
78 = 2(2W - 6) + 2W
78 = 4W - 12 + 2W
78 + 12 = 6W
90 = 6W
15 = W