Of the twelve participants in a certain competition

Dear goodyear2013,
I'm happy to respond. I suppose it's not clear to me whether you have a question and, if so, what it is.

Of 12 participants, half (6) are males, and of these 6 males, half (3) are younger than 18. Thus, so far, we have
3 males younger than 18
3 males older than 18
Now, there must be 12 - 6 = 6 females. Of these 6 females, half (3) are younger than 18. Thus, we have
3 females younger than 18
3 females older than 18

Now, for the 4 competitor collection, we need two of the three males younger than 18, and two of the three females older than 18.
That's 3C2 = 3 choices for the two males, and 3C2 = 3 choices for the females. Apply the Fundamental Counting Principle, explained in this post:
https://magoosh.com/gmat/2012/gmat-quant-how-to-count/
3*3 = 9 possible four-competitor collections.

Does all this make sense?
Mike