In that context, the two sentences have identical meanings.
In both cases, the asker (Ross) is trying to confirm that the listener (Rachel) is aware of something. In both cases, Ross assumes that Rachel will answer: yes.
We know this - that he's looking to confirm his own assumption - because he uses the tag "right?"
You know that she's coming? => Are you aware that she is coming?
You know that she's coming, right? => I believe that you are aware that she is coming; am I right?
But what about that how? Like many short words, how has a variety of uses. Often it's used to ask about the manner or the reason of something: How should I do it? How should I know? But it's also used in some sentences to mean that, or, as the Macmillan Dictionary puts it,
used for referring to a particular fact that you want to mention
I remember how they used to have those huge roaring fires in the winter.
Isn’t it strange how no one ever mentions his name nowadays?
So, the sentence, "you know how she's coming?" could either mean do you know the manner in which she'll be coming? or are you aware that she's coming?
We know which meaning is intended from the context, and also from how the words are spoken.
In the first case (how = in what way), the word how would be stressed, often by pronouncing it with a rising intonation. Because that sentence is a question, there would be two rises, one on "how" and then another on "she's coming." It's also probably more common in this case not to drop the "do" - i.e. it's usually, "Do you know how she's coming" not "You know how she's coming?"
In the latter case (how = that), how is not stressed. The question is pronounced with only one rise. And it's quite uncommon to use "do."
Lastly, this latter case (how = that) is probably most often used to confirm an assumption, and only rarely used when the asker is totally unsure of the answer. That is, "you know how she's coming" almost always means *you know that she's coming, right?" In fact, because we assume this question would be used to confirm an assumption, we usually don't include the tag question ("right?").
That is "you know how she's coming, right?" actually sounds unnatural. We'd expect Ross to say, "you know how she's coming?" and then pause, waiting for Rachel to confirm or disconfirm.