To solve this problem, we need to determine the combined work rate of 3 women and 6 men and calculate how long it would take them to complete the work. Let's analyze the given information:

Step 1: Calculate the work rate of men. 2 men can complete the work in 18 days. Therefore, 1 man's work rate is \( \frac{1}{2 \times 18} = \frac{1}{36} \) of the work per day.

Step 2: Calculate the work rate of women. 6 women can complete the work in 6 days. Therefore, 1 woman's work rate is \( \frac{1}{6 \times 6} = \frac{1}{36} \) of the work per day.

Step 3: Calculate the combined work rate for 3 women and 6 men. The work rate for 3 women is \( 3 \times \frac{1}{36} = \frac{3}{36} = \frac{1}{12} \) of the work per day. The work rate for 6 men is \( 6 \times \frac{1}{36} = \frac{6}{36} = \frac{1}{6} \) of the work per day.

Adding these, the combined work rate for 3 women and 6 men is:

\(\frac{1}{12} + \frac{1}{6} = \frac{1 \times 1 + 2 \times 1}{12} = \frac{3}{12} = \frac{1}{4}\)

Step 4: Calculate the time taken for the combined group to complete the work. Since the combined work rate is \(\frac{1}{4}\) of the work per day, it will take:

\( \frac{1}{\frac{1}{4}} = 4 \) days

Therefore, 3 women and 6 men can complete the work in 4 days.