The philosophy professor confused his students with a complex ethical problem; Meera was the only one who understood it and gave a/an _________ response.

Plausible means "reasonable, credible, sensible" — fitting the context where Meera alone understood the complex problem and gave an apt response.

Why other options fail:

• hirsute = hairy/bearded — describes physical appearance, not responses.
• didactic = preachy, instructively heavy-handed — wrong tone for a student answering a question.
• obsequious = fawning, servile — describes attitude, not the quality of an answer.

Option 4: plausible.