First, you have to make sure you have the correct Global setup for this game. Your completed Global diagram should look something like this:
N K/ N
S K/H J
T H/K /K
(If you have questions about the Global diagram, ask them here: https://forum.powerscore.com/lsat/viewtopic.php?t=11892
Since this is a Local question, we want to create a mini-diagram to incorporate the new Local rule that is being introduced. In this case, we are asked what would happen if K was the leader for one of the committees. The only committee that K can be a leader of is Y (N is always the leader of the other 2 committees). If K is the leader of Y, then H is the only volunteer left who can be the treasurer of Y. So our local diagram looks like this:
S K/H J
T H/K H
The question then asks us "for which of the committees is the assignment of volunteers to positions fully determined?" According to our local diagram, committee Y is the only committee in which the assignment of volunteers to position is fully determined. In committee X, we don't know whether K or H is secretary or treasurer, and in Z we don't know whether M or H is secretary or treasurer. So the answer is (B).
Hope this helps!