Which of the following can extend a period if it occurs as time expires?

The correct answer is that a foul by either team with an accepted penalty can extend a period if it occurs as time expires. According to NFHS rules, if a foul occurs and the penalty is accepted at the end of a period, the period is extended for the execution of the penalty. This means that the clock can be stopped, allowing time for the penalty to be enforced and the play to continue even though the official time for that period has elapsed.

Other options do not extend the period in the same way or at all. A touchdown, while a significant event, does not extend a period if scored as time runs out; the score simply happens, and the period ends unless specific circumstances align with extending play, which scoring alone does not. A timeout does not result in the extension of a period either, as it must be called before time expires for play to be halted. Lastly, a coach's challenge does not influence the timing of a period. It’s critical to understand the specific situations where rules allow for extensions to ensure accurate application during a game.