When she mentioned the new policy, I didn't have a clue what she was referring to.

didn't 是 do not 的缩写形式，表示否定。 have 是动词，意思是"拥有、持有"。 a 是不定冠词，表示"一个"。 clue 是名词，意思是"线索、提示"。 didn't have a clue 是一个固定短语，字面意思是"没有线索"，引申为"完全不知道、毫无头绪"。