Look at each side of the yard separately.
On one side the walk is 4 ft by 49 ft. On the opposite side it is the same. On the other ends the walk is also 4 ft wide but it's length is not 37 ft, it is 37–4-4, which is 29 ft. Those 4 ft subtractions are for the walk that is already on the first two sides. So the area of your walk is
2×4×49 + 2×4×29 = 392+232= 624 sq ft
