You can translate this as "How do you know Li Hong?" or "How did you meet Li Hong?" You would use "How do you know..." if you just found out the person you were talking to knew Li Hong and wanted to find out how they met. This would be used only when you first found out that this person knows Li Hong. You would use "How did you meet..." if what you were most interested in was the circumstances around how they first met. But it can be used even if you already knew the person you were talking to knew Li Hong, but not how they met. Both refer to the past.

iangreen's answer is better, your Chinese is really nice.

Dan seems correct... I suspect the 的 implies past tense, in which case it has more of a sense of "How did you meet" or perhaps more literally: "How did you come to know Li Hong?"