He … be very handsome but i don't like him.

Analyze the question: The sentence is "He __ be very handsome but I don't like him." We need a modal verb that fits the structure "X be ... but I don't like him," which expresses a concession: "Granted, he may be handsome, but..."

Concept: Modal verbs of possibility or concession (may, might, can) are used to admit a point before introducing a contrast with "but."

• "He may/might be very handsome, but I don't like him" means "It is possible or granted that he is handsome, yet I don't like him."
• Shall expresses a promise, command, or future with I/we, so it does not fit here.
• Will can express prediction or habit ("He will be at home by now"), but it does not suit a concessive meaning.
• Can usually expresses ability or general possibility. "He can be very handsome" would suggest he is sometimes handsome, and it is less natural in this concessive sense.

Step-by-step solution:

1. Identify the structure: [Subject] + [modal] + be + adjective + but + contrasting clause.
2. The "but" shows a concession, so we need a modal that grants a possibility.
3. Eliminate shall, because it is wrong for a third-person statement of fact.
4. Eliminate will, because it signals certainty or prediction and does not concede a point.
5. Compare might and can. Might fits best because it concedes a possibility ("he might be handsome, though I don't like him").

Answer: C. might

Tip: When you see a modal followed by "...but...", ask whether the speaker is granting a point before contradicting it. If so, may or might is usually the best choice. Remember the pattern: "He may be rich, but he is not happy."