PLEASEE HELPPPP!!!!! ASAP SEE ATTACHED!

Short answer: C
Let's start with the pen. 
The length is x
The width is 3 more.= x + 3 
Perimeter of the pen = 2L + 2W
P = 2 L + 2W
P = 2*x + 2(x + 3)
P = 2x + 2x + 6
P = 4x + 6. Leave that for now.

Area of the pen without the doghouse = x(x + 3)
Area of the pen without the doghouse = x^2 + 3x
Area with the doghouse x^2 + 3x - y = 178 (that's his running around space.

Go to the dog house for a Moment
The perimeter of the doghouse and the area are equal and we are told to make them both y.
Area = y
Perimeter = y

Combined facts.
The perimeter of the Pen is three times larger than that of the dog house.
4x + 6 = 3y

The area of the Pen - The area of the doghouse = 178
x^2 + 3x - y = 178

Now what happens is that you have to juggle these two equations so they look like your answer
x^2 + 3x - y = 178
4x + 6 = 3y  Subtract 3y from both sides.
4x - 3y + 6 = 0 Subtract 6 from both sides.
4x - 3y = - 6

Answer C