You cannot completely "delete" questions that have been asked on eNotes.  Only eNotes staff members have the power to do this.

The idea or purpose of this is to create an archive of questions and answers that will inevitably pop up if another student were to do a Google (or other) search for a similar question.  Notice how every question is "tagged with" certain keywords or phrases.  This makes each question "Search Engine Optimized" - one, so that other students or teachers needing help on similar assignments can get it.  Also, this is to advertize for this resource.  I'm sure you've noticed when doing a Google Search, for example, that eNotes is often one of the top suggested sights for literature questions (it certainly is for teachers seeking lesson plans or test questions).  This "popularity" (for lack of a better term) is a major reason why eNotes is able to continue serving students and teachers for free or at a very low price.

I'm not sure why you'd want to delete a previous question (unless you are like me, and once you've used something you like to clean house, so to speak) but if the question was never answered, or simply worded weirdly, you can always go in and "edit" it - hoping to get more information or make the question more clear.