The area of the garden = \(x * y = xy\)
The area of the garden + walkway = \((x+4)(y+4)\); since the width of the walkway is 2 feet wide hence 2+2 = 4 feet will be added to length and width of the garden for a combined length and breadth as the garden is surrounded by walkway

the area of walkway = \((x+4)(y=4) - xy\)
simplifying the area of the garden + walkway = \(xy + 4x + 4y + 16\)
therefore, area of the walkway = \(xy + 4x + 4y + 16 - xy = 4x + 4y + 16\)
option D
_________________

The garden (interior rectangle) is x feet wide so the larger rectangle is (x + 4) feet wide. Similarly, the garden’s length is y feet, so the exterior rectangle’s length is (y + 4) feet long. Thus, the area of the larger rectangle is (x + 4)(y + 4). The area of the garden itself is xy. We can thus create the expression for the area of the walkway as the difference of the two areas::

(x + 4)(y + 4) - xy

xy + 4x + 4y + 16 - xy

4x + 4y + 16

Answer: D
_________________