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.