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 $24{\mathrm{\pi r}}^2\mathrm{T}.$