Concept:Modal auxiliary verbs (like will, can, could, etc.) must always be followed by the base form (V1) of the verb.
Rule / Clue:After a modal, do not use the third-person singular form (like teaches) or any other tense. The verb must stay in its simplest form.
Explanation:The original segment "will teaches" is wrong because "will" is a modal, but "teaches" is the third-person singular form. The correct base form is "teach".
Option B "can teach" is the most suitable here. It shows that the younger brother has the ability to teach graduate students. In many English proficiency tests, "can" is preferred to express capability in a professional context.
Option A "will teach" is grammatically correct, but "can teach" fits better when the sentence focuses on ability.
Option C "could teach" suggests past ability or a conditional possibility, which does not match the simple factual statement.
Option D "would have teach" is incorrect because "would have" must be followed by the past participle "taught", not the base form "teach".
Answer:B. can teach