To determine how many hours a day 15 men must work to complete the same amount of work in 12 days, we can use the concept of man-hours.

1. Calculate the total man-hours required to complete the work:

If 10 men working 6 hours a day can complete the work in 18 days, the total man-hours required is:
$$\text{Total Man-Hours}=\text{Number of Men}\times \text{Hours per Day}\times \text{Number of Days}$$
$$\text{Total Man-Hours}=10\times 6\times 18=1080\text{ man-hours}$$

2. Determine the number of hours per day required for 15 men to complete the work in 12 days:

Let $h$ be the number of hours per day that 15 men need to work. The total man-hours for 15 men working $h$ hours a day for 12 days is:
$$\text{Total Man-Hours}=15\times h\times 12$$
Set this equal to the total man-hours calculated:
$$15\times h\times 12=1080$$
$$180h=1080$$
$$h=\frac{1080}{180}=6$$


15 men must work 6 hours a day to complete the work in 12 days.

The correct answer is A. 6.