Concept:After the helping verbs do / does / did (including "did not"), the main verb is always in its base form.
Solution:"did" already shows the past tense, so the main verb must not show tense again.
The base form of the verb is "meet": "The messenger did not meet anyone in the house."
B. "met" marks the past a second time ("did not met" is wrong).
C. "meets" is the present form with -s, which cannot follow "did".
D. "meeting" is the -ing form, which needs "was" or "is", not "did".
Key point: Only one verb in the group shows tense: "did not meet", "does not meet", "do not meet".
Answer:Option A (meet)