You can't find the actual area of the walkway, because you don't know the actual size of the garden. So you're supposed to be finding the area of the walkway as an "expression" of the width.
The area of the garden is width times length: w*(w+4), or w^2 +4w.
The width of the garden plus the walkway would be w+4, or the width of the garden plus two feet of walkway on one side plus two more feet of walkway on the other side. You would also add 4 to the length of the garden to get the length of the garden plus the walkway, or w+8. So, the area of the garden and the walkway together is (w+4)*(w+8), or w^2 + 12w + 32.
Now, subtract the area of the garden by itself from the area of the total space: (w^2 + 12w + 32) - (w^2 + 4w). Simplified, this means that the area of just the walkway would be 8w + 32.
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