The surface area of a cylinder is given by
[tex]A_A = 2\pi rh[/tex]
which is the surface area of cylinder A.
To compute the surface area of cylinder B, we have to map [tex](r,h)\mapsto (2r, 2h)[/tex] and we have the following formula
[tex]A_B = 2\pi(2r)(2h)[/tex]
If we manipulate the second expression, we have
[tex] A_B = 8\pi rh[/tex]
Which implies
[tex]\dfrac{A_B}{A_A} = \dfrac{8\pi rh}{2\pi rh} = 4 [/tex]
