Explanation:

- Work Rates:

- X completes the work in 6 days, so X’s work rate is 1/6 of the work per day.

- Y completes the work in 12 days, so Y's work rate is 1/12 of the work per day.

- Alternating Work Pattern:

- Day 1: X works, completing 1/6 of the work.

- Day 2: Y works, completing 1/12 of the work.

- Total work completed in 2 days = 1/6 + 1/12 = 1/4 of the work.

- Completion Calculation:

- In 6 days, they complete 3/4 of the work (as 1/4 is completed every 2 days).

- On Day 7, X works and completes 1/6 of the work.

- By end of Day 7, total work done = 3/4 + 1/6 = 11/12 of the work.

- Final Day:

- On Day 8, Y works and completes the remaining 1/12 of the work.

- Total = 1 (Whole work completed)

- Correct Answer: Option 3 - 8 Days