Explanation:

- A completes $\frac{2}{3}$ of the job in 6 days. So, A completes $\frac{2}{3}÷6=\frac{1}{9}$ of the job per day.

- B completes $\frac{1}{3}$ of the job in 8 days. So, B completes $\frac{1}{3}÷8=\frac{1}{24}$ of the job per day.

- C completes $\frac{3}{4}$ of the job in 12 days. So, C completes $\frac{3}{4}÷12=\frac{1}{16}$ of the job per day.

When all three work together for 4 days:

- They complete $(\frac{1}{9}+\frac{1}{24}+\frac{1}{16})\times 4=\frac{1}{3}+\frac{1}{6}+\frac{1}{4}$.

- Simplifying this, they complete $\frac{37}{72}$ in 4 days.

Remaining work:

- Total job = 1. They completed $\frac{37}{72}$ in 4 days.

- Remaining work = 1 - $\frac{37}{72}=\frac{35}{72}$.

B alone completes $\frac{1}{24}$ per day. To complete $\frac{35}{72}$ remaining work:

- Time required = $\frac{35}{72}÷\frac{1}{24}=\frac{35}{72}\times 24=\frac{35}{3}\approx 11.67$ days.

Since 11.67 days exceeds any of the given options for B to finish the job alone and there might be a misunderstanding, the conclusion is the presented options might not exactly match the calculated time. Your answer seems incorrect for the given options, indicating some assumptions might need adjustment.