According to the question,

A does the work in x days and B can does the same work in 2x days.

$=\frac{1}{x}+\frac{1}{2x}=\frac{1}{4}$

On multiplying both the sides with x we get,

$$\begin{gathered} \Rightarrow 1+\frac{1}{2}=\frac{x}{4} \\ \Rightarrow \frac{3}{2}=\frac{x}{4} \\ x=\frac{4\times 3}{2}=6 days \end{gathered}$$

∴ B will finish the work in 2x days or in 2×6=12 days.

 Hence option A is the correct.