Haha, to add on to Verity:
Here's a neater version of my diagram
Sorry that the bottom isn't that clear, the columns are labeled F, W, Sp, Su.
From here, it is a simple matter of filling in every hypothetical presented in the answer choices. You quickly discover that the limiting rule here is the first one: Each child participates in exactly four different sports. I'll only demonstrate one incorrect answer choice to show you why it doesn't work:
A: Put N in the M slot for fall and O in the R slot for spring. Now try to fill in the rest. You run into an immediate problem: O is now filled in for V (summer) and R (spring), and the only sport left for O is H in winter. O can't go anywhere in the fall, because the only open slots are V and R.
The other incorrect answer choices are wrong for the same reason.
When you get around to inputting C, you realize that the entire diagram works when you try to fill in around it. Put N in the M slot for spring and O in the M slot for fall. Now you can put another O in the R for fall and the H for winter, which leaves N open to a V in winter and a two different possible options for spring and summer. There is nothing that disqualifies this scenario. Therefore it is the correct answer.
FYI, edit out the text of the question from the post. You're technically not allowed to quote extensively from LSAC material on TLS.
Hope that helped!
Edit: Scooped by verity's edit! I'll leave this up in case it is helpful.
Another edit: After looking at verity's, that diagram is more efficient. Use that one! Mine works but is slow.