First, I made a mistake and we need to correct it. The radius of the lake is indeed 120, but the radius of the outer circle is not 123, it is 126. The walkway is 6 feet in width, you don't need to half it, so use
Pi (126^2 - 120^2) for the area but otherwise your answer is correct.
For the second part where the walkway is doubled in width, do the same thing but use 132 for the outer radius.