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The correct answer to this problem would be the word theirs, the first one.
The usage of their/s is kind of a tricky one since it depends on what it usually is pertaining to in the previous lines. In this problem, it would refer to our presentation. If another word, let's say presentation, is added after the blank, then the answer would be their. In this case, there isn't anything after it so the answer would be theirs.
Those that have apostrophes on them aren't an option since it isn't applicable in this situation.
You should write about when you first started taking care of the pet and fedding it and playing games with the pets toys and how you watched it
