Let's assume the width of the swimming pool is "x" meters.
The length of the swimming pool would then be "x + 12" meters.
Considering the walkway surrounds the pool on all sides, the total width including the walkway would be "x + 2 + 2" meters (two sides of the walkway).
The total length, including the walkway, would be "x + 12 + 2 + 2" meters.
The area of the walkway is given as 168 square meters, which can be represented as:
Area of the walkway = Total area including the walkway - Area of the pool
168 = (x + 2 + 2) * (x + 12 + 2 + 2) - x * (x + 12)
168 = (x + 4) * (x + 16) - x^2 - 12x
168 = x^2 + 16x + 4x + 64 - x^2 - 12x
168 = 8x + 64
8x = 168 - 64
8x = 104
x = 104/8
x = 13
Therefore, the width of the swimming pool is 13 meters, and the length of the swimming pool is 13 + 12 = 25 meters.