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Solution
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A modal verb is a verb which expresses the attitude of the speaker to what is being said.
The given sentence in the passage needs a modal verb of future tense having a strong certainty of refusal.
Option D is the correct answer because "won't be able to" serves as an expression of caution in the future form in this sentence. Whereas in option A,B and C do not serve the necessary mood. Therefore, "won't be able to" is the appropriate answer.
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