If 6 men or 8 women can finish a work in 12 days, 9 men and 12 women will finish the work nearly?

4 days to complete the work.

Explanation:

6 MEN OR 8 WOMEN

means that each man completes the 1 / (6*12) of the work per day

OR each women completes 1 / (8*12) of the work per day

9 MEN AND 12 WOMEN completes ...

9 * 1 / (6*12) + 12 * 1 / (8*12) of the work per day.

Note that we add these 2 fractions because of the word 'AND'.

that gives us a simple fraction of 1/4 of the work per day.

Thus reversing it, gives you time taken = 4 days to complete the work.