According to the question,

A+B can complete a work in 3 days.

In 2 days,

(A+B) can complete⇒ $2\times \frac{1}{3}=\frac{2}{3}$ of the work

A alone in complete⇒ $1-\frac{2}{3}=\frac{1}{3}$of the work

B alone can complete⇒ $\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$of the work

So in 1 day B can complete  ⇒$\frac{1}{6}$ of the work. Therefore, B alone will take 6 days to complete the work.

Hence option B is correct