8men and 6 women arrive separately in a random fashion to a meeting. what is the probability that the first 4 people to show up are men?

Ok, so here:
Remember for basic probability, you have to do: Probability=Events/Possible outcomes. For multiple events, you have to multiply all together.

The probability the first guy that shows up will be 8/14, because out of the 14 people, 8 of them are men. This however isn't your answer, note the question says "Separately"
The probability the second person that comes in is a dude is 7/13, because you have the first guy already in, and only 13 left.
The third person to come in being a dude has a probability of 6/12
The fourth person to come in being a dude has a probability of 5/11

When you have multiple events, the way to solve probability is to find the chances of each as a fraction, then multiply them together.

8/14 * 7/13 * 6/12 * 5/11=1680/24024
1680/24024=168/168 (168 goes into both)
Your final answer is 10/143
~Hope this helps!