Step 1: Understand the correct form of the verb.
In this sentence, the phrase "excuse me for" is typically followed by a gerund (the "-ing" form of a verb) to indicate the reason for the apology. "Being late" is the correct form.
Step 2: Analyze the options.
- (A) not be late: Incorrect. This is an infinitive form, which is not used after "excuse me for."
- (B) late very much: Incorrect. This is an awkward and incorrect phrasing. The adjective "late" does not work here in this structure.
- (C) being late: Correct. "Being late" is the correct gerund form used after "excuse me for" to explain the reason for the apology.
- (D) very much late: Incorrect. This is another awkward phrasing and does not fit grammatically.
Step 3: Conclusion.
The correct phrase is "being late," which follows the grammatical structure for excusing oneself for an action.