If there are 4 pairs of twins, and a committee will be

What do you mean by FCP? Factorial, combinations, permutations?
But these are typical questions for the use of such mathematical tools.
Anyway, you have to use at least the multiplication principle, you cannot do without it.

Here is an approach:
The first member can be anybody, so 8 possibilities.
The second member cannot be the sibling of the previous member, therefore 6 possibilities (anybody from the remaining 3 pairs).
Finally, the third member, can be chosen from the remaining 2 pairs, so 4 possibilities.
This would give us 8*6*4 possibilities, but in this case we don't care about the order in which we choose them, we have to divide the product we obtained by 6(=3!), which is the number of possibilities we can chose the same three distinct members, say ABC (it can be BAC, CAB,...). You can count those possibilities for such a small number as 3, but why avoid permutations? Is it better to start listing the possibilities instead of just accepting the already proven result?

So, the correct answer is 8*4=32.

Answer A.

Avoiding FCP, you can start listing all the possibilities, solve just by brute force. FCP were developed exactly to deal with counting problems, to avoid lengthy counting. There are no other methods in mathematics for these type of questions.