The radius of a soap bubble is r and the surface tension of soap solution is T. Keeping the temperature constant, the extra energy needed to double the radius of the soap bubble by blowing, is 

The energy needed to change causes the bubble's size to expand,

Surface tension of the soap solution =T, 

initial radius of the soap bubble =r, 

and final radius of the soap bubble =2r

We know that the energy required to blow a soap bubble with radius r, ${\mathrm{E}}_1=2\times 4{\mathrm{\pi r}}^2\times \mathrm{T}=8{\mathrm{\pi r}}^2\mathrm{T}$

Energy required to blow radius 2r ${\mathrm{E}}_2=2\times 4\mathrm{\pi }{\left(2\mathrm{r}\right)}^2\mathrm{T}=32{\mathrm{\pi r}}^2\mathrm{T}$

Extra energy needed is

 ${\mathrm{E}}_2-{\mathrm{E}}_1=32{\mathrm{\pi r}}^2\mathrm{T}-8{\mathrm{\pi r}}^2\mathrm{T}=24{\mathrm{\pi r}}^2\mathrm{T}$

Hence the correct answer is $24{\mathrm{\pi r}}^2\mathrm{T}.$