How to say "I like listening to them talk about .." in Chinese
Hello, I am trying to find out the correct characters to say in Chinese "I like listening to them talk about...". I want to be able to say "I like listening to her talk about her daily life". This is my attempt at this sentence in chinese, I was wondering if it was correct - 我很喜欢听她说话她的日常生活."
Thank you for any replies.

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Hi BHT, that is incorrect. You could say things like “我喜欢聆听她的日常生活” or “我很喜欢听她说她的日常生活.”, but as Pearl Liang said, it would be better to say 我很喜欢听她分享她的日常生活, for it does not sound natural to say "我很喜欢听她说她的日常生活" though it is correct. 
have a nice day and hope this helps.

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Hi BHT, what Kai said is absolutely right, just wanna add one more natural way to say that is “我很喜欢听她聊……”.

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Thank you for the help everyone! I really appreciate it.

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I like listening to her talk about her daily life 我很喜欢听她（说/讲）她的日常生活。“say”can be translated “说or讲"。But I think this expression will be better：我很喜欢听她分享（share）她的日常生活。