To anonymously edit a question, you will need to use the Anonymous Edit Link. This includes anonymously making edits to the question, its details, or the applied topics. All edits made on the public question page will be associated with your name. If you make a public edit, you will not be identified as the original question asker.
Note: if you want to delete your anonymous question, you still need to follow our general policy on question deletions. This means that an anonymous question cannot be deleted if the question page has already exceeded a certain level of activity. To learn more about this policy, please refer to: http://www.quora.com/What-is-Quoras-policy-on-question-deletion