The perimeter of a rectangle is the distance completely around the rectangle. Imagine you're walking around the rectangle starting from a corner. You'd walk up the length L, then turn and walk along the width W, then turn and walk another length L, then turn and walk another width W to get back to where you started. So you walked 2 lengths and 2 widths, The perimeter then is computed as:
Perimeter of a rectangle = 2L + 2W = 2(L + W)
In your problem, the perimeter is 64 feet and the width is 1/2 the length minus one foot, which is W = (1/2)L - 1. Looks like you almost got it right. Now plug (1/2)L-1 in for W in the Perimeter equation above and let me know what you get (in the comments).
[Teaching moment. Please let the student complete the solution. Thank you.]