Explanation:

- A, B, and C together can complete the work in 6 days. Therefore, their combined work rate is 1/6 of the work per day.

- A and B together can finish the work in 12 days. Thus, their combined work rate is 1/12 of the work per day.

- B alone can accomplish the work in 18 days, which means B's work rate is 1/18 of the work per day.

- To find the work rate of A and C together, we need to determine the individual work rates of A and C.

- From A, B, and C's total work rate (1/6) and A and B's combined work rate (1/12), we can deduce that C's work rate is (1/6 - 1/12) = 1/12.

- Knowing B's work rate (1/18) and A and B's combined work rate (1/12), we can deduce that A's work rate is (1/12 - 1/18) = 1/36.

- So, A and C's combined work rate is (1/36 + 1/12) = 1/9.

- Therefore, A and C together can complete the work in 9 days.

Option 1 - 9 days is the correct answer.