The best translation of- ‘আমি তার সাথে কথা বলি না’।

1. Meaning Preservation: The phrase "on speaking terms" in English refers to having a relationship in which two people are willing to speak to each other. This accurately captures the meaning of the Bengali sentence, which indicates a lack of willingness to communicate with the person referred to as "তার" (him).

2. Idiomatic Expression: "On speaking terms" is an idiomatic expression in English that specifically conveys the idea of being willing to communicate or engage in conversation with someone. This idiomatic usage aligns well with the context of the original Bengali sentence.

3. Grammatical Correctness: The translation "I am not on speaking terms with him" maintains grammatical correctness in English. It uses the appropriate preposition "on" in conjunction with the phrase "speaking terms" to convey the intended meaning accurately.