correct answer is: d) 16 days

Explanation

Here, Hours and days are Inversely Proportional.
\therefore\;6\;:\;8\;:\;:\;12\;:\;x
\rightarrow\large\frac{6}{8}=\frac{12}{x}
\rightarrow 6x=12\times8
\rightarrow x=\large\frac{12\times8}{6}
\rightarrow x=16 days
\therefore 16 days will be required to complete the work.
Ans: They will take 16 days to complete the work.

An alternative way to phrase this particular math query is possible:

1. If a certain number of men can complete a task in 12 days, working 8 hours per day, how many days will it take to complete the task if they work 6 hours per day?
2. Given that a certain number of men can complete a task in 12 days working 8 hours per day, how long will it take to complete the task if they work 6 hours per day?
3. How many days are needed to complete a task if a certain number of men, who can complete it in 12 days working 8 hours per day, work 6 hours per day?