Explanation:

- A and B together can complete the work in 12 days. This means their combined work rate is 1/12 of the work per day.

- A alone can finish the work in 18 days. Therefore, A's work rate is 1/18 of the work per day.

- To find B's work rate, subtract A's work rate from the combined work rate:

- Combined work rate: 1/12

- A's work rate: 1/18

- B's work rate: (1/12) - (1/18).

- Calculate B’s work rate:

- The common denominator for 12 and 18 is 36.

- Convert the rates: (3/36 - 2/36) = 1/36.

- So, B alone can do the work in 36 days.

- Option 1: 36 days

- Option 2: 6 days

- Option 3: 24 days

- Option 4: 12 days