correct answer is: a) 20 days

Explanation

2 men = 4 women
\therefore 1 men =\large\frac{4}{2} women
\therefore 4 men =\large\left(\frac{4\times4}{2}\right) women
\rightarrow 8 women
And, 12 men =\large\left(\frac{4\times12}{2}\right) women
\rightarrow 24 women.
So that,
4 men and 7 women equal to:
\left(8+7\right)=15 women.
And, 12 men and 6 women equal to:
\left(24+6\right)=30 women.

Now,
15 women can do a work in 40 days
\therefore 1 women can do a work in =\left(40\times15\right) days
\therefore 30 women can do a work in =\large\left(\frac{40\times15}{30}\right) days
\rightarrow 20 days.
Ans: 12 men and 6 women will take 20 days to finish the work.

Another form of this specific math question exists:

1. If the work output of 2 men equals that of 4 women, and 4 men along with 7 women can complete a task in 40 days, how many days will it take for 12 men and 6 women to finish the same task?
2. How many days will it take for 12 men and 6 women to complete a task if 4 men and 7 women typically finish it in 40 days, and the work output of 2 men equals that of 4 women?
3. If a task can be finished by 4 men and 7 women in 40 days, and the work of 2 men equals that of 4 women, how many days will it take for 12 men and 6 women to complete the task?
4. Suppose a task normally requires 4 men and 7 women to complete in 40 days, and the work output of 2 men equals that of 4 women. How long will it take for 12 men and 6 women to finish the task?