Step 1 :First, consider the group of men as a single entity and the group of women as another single entity. So, we have two entities to arrange in two places, which can be done in \(2!\) ways.
Step 2 :Next, arrange the three men among themselves and the three women among themselves. Each of these can be done in \(3!\) ways.
Step 3 :According to the fundamental counting principle, the total number of ways these people can sit is the product of the number of ways to perform each of these tasks.
Step 4 :So, the total number of ways is \(2! * 3! * 3!\) = \(2 * 6 * 6\) = \(72\).
Step 5 :Final Answer: The total number of ways these people can sit if all men must sit together and all women must sit together is \(\boxed{72}\).