This is an interesting question and I am not sure what motivates you to ask it, but the only way to make a question private on the eNotes site is to ask a question directly to one of the eNotes educators via e-mail. This is not likely to produce the results you would like, since the educators are under no obligation to answer e-mailed questions.
Posting your question publicly is the quickest, most efficient way to ensure that it will be answered. Educators on this site are all looking for ways to be helpful and are always willing to share their expertise with students or teachers who have questions. An eNotes membership is a wonderful resource for students because they have access to thousands of pages of helpful information as well as hundreds of thousands of questions in all areas that have already been asked and answered.