A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days.

Time taken by $\mathrm{A}$ and $\mathrm{B}$ to finish a piece of work $=6$ days

Work done per day by $\mathrm{A}$ and $\mathrm{B}=\frac{1}{6}$

Time taken by $\mathrm{A}$ alone $=9$ days

Work done per day by A alone $=\frac{1}{9}$

Work done per day by $\mathrm{B}=($ work done by $\mathrm{A}$ and $\mathrm{B})-($ work done by $\mathrm{A})$

$=\frac{1}{6}-\frac{1}{9}=\frac{3-2}{18}=\frac{1}{18}$

$\therefore \mathrm{B}$ alone will take 18 days to complete the work.