Air is pumped into a soap bubble of radius r , doubling its radius....

A soap bubble has two free surfaces, an inner surface and an outer surface.

Initial surface area of the soap bubble, $A_1 = 2 \times 4\pi r^2 = 8\pi r^2$

Final radius of the soap bubble is $2r$.

Final surface area of the soap bubble, $A_2 = 2 \times 4\pi (2r)^2 = 32\pi r^2$

Change in surface area, $\Delta A = A_2 - A_1 = 32\pi r^2 - 8\pi r^2 = 24\pi r^2$

Work done in increasing the radius is equal to the change in surface energy.

$W = S \times \Delta A = S \times 24\pi r^2 = 24\pi r^2 S$