Q:

Which "not" is not in the proper place: "Not only does (not) she (not) know, but also ..."

I know that whenever we bring "not only" at the beginning of a sentence, what comes after it has to be in question form.
Now, I'm having a problem with the negative form of this question.
Which one of the following sentences is correct?

Not only doesn't she know, but also ...

or

Not only does she not know, but also ...

A:

This is what mathematicians call a pathological example - one sought out to test the rules to their limit. So on the one hand this specific case may not be covered in the grammars but on the other hand we may be able to learn something about grammar by looking at it.
First we have to look at the question form without the "not only". We find that there are two valid forms:

Does she not know?
  Doesn't she know? 

Why we are allowed different word order when we want to abbreviate I have no idea. Maybe it is answered in another question. 
But whatever the reason, it is nonetheless a fact. 
It is another fact (and perhaps there is an explanation on this site for this too but it may be something to do with this) that you use the inverted (or question) form after "not only" so both forms given in the question are logically valid. And indeed they both sound fine to me too. 

