Here's how to correctly fill in the pronouns for proper agreement:
Everyone is excited for the fall carnival. They all have to work together in order for it to be a success. Carter and Emma are in charge of blowing up the balloons, their least favorite task. It takes up so much of their time. On the other side of the field, Sam is practicing for the dance competition. If he doesn't practice, Sam could embarrass himself. The last to arrive are Destiny and Hudson with the shirts to pass out. As long as everyone does their part, the carnival will be a success!
(Note: The pronoun "he" for Sam is inferred and not included in your initial list of responses, as "he" is not found in the provided options. If "he" were an option, it would be used instead of "they." If you want to keep it strictly to the provided options, use "they" and "them.")