Let L=the length of the rectangular backyard, and let W=the width of the rectangular backyard, and A=the area of the backyard.

Now the first sentence says that the length is 6 more than the width: We can write this as L = W + 6.

The second sentence says that the perimeter of the backyard is 44 feet: We can write that as 2L + 2W = 44.

Substituting for L (from the first equation) into the second equation: 2(W + 6) + 2W = 44

or, using the distributive law, 2W + 12 + 2W = 44, or 4W + 12 = 44.

Subtract 12 from both sides of the equation to get 4W = 32. Now divided both sides of the equation by 4, to get W=8.

Substitute this value back into the first equation to get L = W + 6 = 8 + 6 = 14

So, now we have L = 14 and W = 8.

The third sentence asks for the area of the backyard, so A = L x W.

Substituting for L and W, we finally arrive at A = 14 x 8 = 112 square feet.