Without any examples, I really don't think we can help you. I wonder if it's more a case of accent or pronunciation than "broken" English, but of course I didn't hear what you did. I guess the best tactic is to politely ask them to repeat themselves. I use excuses like outside noise, a bad connection (if you're on the phone), or I say that I'm "a little hard of hearing" if I want to tactfully ask the speaker to repeat what they've just said. Also, ask if they could send a follow-up email or put the ideas/decisions/requests in writing. Of course this is good business practice, but it also covers you if you didn't fully follow the conversation.

That's a good question. I can't answer it sorry!