A and B can complete a piece of work in 12 days and 18 days respectively. They start working together, but after 4 days, A leaves the work. In how many days will B alone complete the remaining work?

The correct answer is 8.

Step 1: Determine the daily work rate of A and B.
Let the total work be represented as 1 unit.
Work done by A in 1 day = $\frac{1}{12}$
Work done by B in 1 day = $\frac{1}{18}$

Step 2: Calculate the work done by A and B together in 1 day.
Combined work in 1 day = $\frac{1}{12}+\frac{1}{18}$

Taking the Least Common Multiple (LCM) of 12 and 18, which is 36:
Combined work in 1 day = $\frac{3+2}{36}=\frac{5}{36}$

Step 3: Calculate the total work completed in 4 days.
Since A and B worked together for 4 days before A left:
Work completed in 4 days = $4\times \frac{5}{36}=\frac{20}{36}=\frac{5}{9}$

Step 4: Calculate the remaining work.
Remaining work = $1-\frac{5}{9}=\frac{4}{9}$

Step 5: Calculate the time taken by B alone to finish the remaining work.
Days required by B = $\frac{\text{Remaining Work}}{\text{B's 1-day Work}}$

Days required by B = $\frac{4/9}{1/18}=\frac{4}{9}\times 18=4\times 2=8$ days.

Therefore, B alone will complete the remaining work in 8 days.