Explanation:

- A's work rate: A can complete the work in 30 days. This means A completes 1/30 of the work in one day.

- B's work rate: B can complete the work in 18 days. Thus, B completes 1/18 of the work in one day.

- A works alone for 6 days: Therefore, A completes 6 × (1/30) = 1/5 of the work during this period.

- Remaining work: After A's initial 6 days, 4/5 of the work remains.

- A and B work together: Their combined work rate is 1/30 + 1/18 = 8/90 = 4/45 of the work per day.

- Days to complete remaining work: (4/5) / (4/45) = 9 days.

- Total days for the whole work: 6 days (A alone) + 9 days (together) = 15 days.

- Correct Answer: Option 2, 15 days