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Compare these two sentences:
He cannot do that.
And:
He cannot possibly do that.

I know for sure that there's a difference between them but it's so hard to tell, at least for me.
Please make it clearer. Thank you very much.
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To me, the word 'possibly' adds emphasis and suggests that even if it is theoretically possible for him to do that, he cannot.
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I agree with Yankee