Explanation for being late
There are a few modal verbs that can be used to complete the sentence "but only if you ___ explain why you are so late?" Here is a detailed explanation using modal verbs:

Must
- If you must explain why you are so late, it shows a sense of necessity and obligation. It implies that providing a reason for your tardiness is required in this situation.

Should
- If you should explain why you are so late, it suggests a recommendation or advice to give an explanation for your lateness. It indicates that it would be the right thing to do in this circumstance.

Need to
- If you need to explain why you are so late, it emphasizes the requirement or necessity of providing a reason for your delay. It conveys that an explanation is essential in this scenario.

Have to
- If you have to explain why you are so late, it implies a strong obligation or compulsion to give a justification for your tardiness. It indicates that there is no choice but to provide a reason in this instance.
In conclusion, using modal verbs like "must," "should," "need to," or "have to" in the sentence "but only if you ___ explain why you are so late" emphasizes the importance and necessity of providing a reason for being late. It highlights the requirement to offer an explanation in this specific situation.