The area of the park is 48*36=1728 sq m. The path runs around the inside of this area, reducing it by 3m all the way round, so the length and width are each reduced by twice the width of the path.
The dimensions of the enclosed area are 48-6=42m and 36-6=30m, so the enclosed area is 42*30=1260 sq m and the area of the path is 1728-1260=468 sq m.
The area can also be calculated as the sum of two pairs of identical sized strips: 2*48*3+2*30*3=288+180=468 sq m.