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Hi, help me with the sentences below.

I think each a-b has almost the same meaning respectively.

Any suggestion is welcome.

1a) She should have known better than to listen to him.

1b) She should have known better not to listen to him.

2a) I had difficulty understanding him.

2b) I had difficulty to understand him.
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1b and 2b are not correct. 1a and 2a are what you want.

You can say She should have known better than not to listen to him, but that's the opposite of 1a.

CJ
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Thanks for the answer, but could I ask you why they are incorrect?
They are incorrect because they break the rules of English grammar.

The idiom is to know better than. The word than is part of the expression.
The words I had [difficulty / trouble / a problem / a hard time] are followed by an -ing word.

CJ
Is it incorrect to consider "to understand him" as an infinitive functioning as an adjective which modifies the word "difficulty"?
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Is it incorrect to consider "to understand him" as an infinitive functioning as an adjective which modifies the word "difficulty"?

No, that would not be incorrect. In fact, if English allowed infinitives after the word difficulty, that would be exactly the right way to analyze the situation.

CJ