This is the problem:

The greenhouse I am building for my wife is 6 feet longer than it is wide. I only have enough concrete for 56 feet of foundation (the number of feet in the foundation is equal to the perimeter of the building). What are the possible values for the length of the building?

Do I use this type of solution to figure it out?

P=2L+2W=2(L+W)

I AM STUMPED!!

Yes, that's the right equation. But you also know that the building is 6 feet longer than it is wide, which tells you that:

L=W+6

Now you can substitute this for the L in your equation, and solve.

This is the problem:

The greenhouse I am building for my wife is 6 feet longer than it is wide. I only have enough concrete for 56 feet of foundation (the number of feet in the foundation is equal to the perimeter of the building). What are the possible values for the length of the building?

Do I use this type of solution to figure it out?

P=2L+2W=2(L+W)

I AM STUMPED!!!!!
When I get down to the bottom, I get
P=4W+12=4W+12
Am I missing something?

Looks good to me. Don't forget that you know the perimeter (P) is 56 feet. Now solve for W. Then sub your value for W back into the earlier equation L =W+6 to find L.

If you try to solve for w, does it work out to be 0? I am losing my marbles over this one!!

You were on the right track.

4w+12=56

w=11

Therefore, L=17

Your greenhouse has dimensions W=11 and L=17

Area: 11*17=187 square feet