hang on (one's) words
To listen very closely, intently, or with obsequious attention to what one is saying. The politician was so charismatic that he had even his detractors hanging on his words. She had the whole audience hanging on her words by the end of her presentation.
hang on someone's words
Listen very attentively to someone. For example, You don't need to hang on his words-just remember the gist of it. It is also put as hang on to every word, as in Whenever Mother read their favorite book to them, the children hung on to every word.