A can complete a piece of work in 12 days, and B can complete the same work in 16 days. If they work together, how many days will it take to complete the work?

Explanation:

1. Work done by A in 1 day: $\frac{1}{12}$ of the work.
2. Work done by B in 1 day: $\frac{1}{16}$ of the work.
3. Work done together in 1 day: $$\frac{1}{12}+\frac{1}{16}=\frac{4}{48}+\frac{3}{48}=\frac{7}{48}$$ of the work.
4. Total days required: $$\text{Days}=\frac{1}{7/48}=\frac{48}{7}\approx 6.857\text{ days}$$

Rounded to the nearest whole number, it takes approximately 6 days, so the correct option is A. 6 days.