Explanation:

- A can complete the job in 6 days. Therefore, A's work rate is 1/6 of the job per day.

- B can complete the job in 12 days. Therefore, B's work rate is 1/12 of the job per day.

- Both A and B work together for the first 3 days. Together, they complete (1/6 + 1/12) * 3 = (1/4) * 3 = 3/4 of the job in these 3 days.

- After 3 days, A leaves, and the remaining work is 1 - 3/4 = 1/4 of the job.

- B, working alone, can finish this remaining work. B's work rate is 1/12 per day, so it takes B 3 more days to finish the remaining 1/4 of the job.

- The total time taken is 3 days (together) + 3 days (B alone) = 6 days.

Option 3: 6 is the correct answer.