Ask HN: Dealing with thick english accents, what do you do?

I am occasionally on phone calls and in meetings where the guests on the call may speak english as a second language. During these calls, I make a conscience effort to try to understand what the caller means, but unfortunately, sometimes the accent is simply too thick for me to understand.

In one occasion, I did my best to get the general question, but I didn't want to be offensive and say I didn't understand. I ended up answering the questions wrong and was sharply criticized at the end of the call.

What is the most professional way you can handle a situation like this eloquently?