Log in to your Tumblr blog and then click the “Inbox” icon. You’ll see a list of questions that other Tumblr users have asked you. Click the “Answer” link on any Asks you want to answer. A new text box appears under that specific question. Type your answer in the text box and then click the “Answer Privately” button located under the text box, next to the Publish button. This sends a private answer to the inbox of the Tumblr user who sent you the Ask instead of publishing it publicly on your Tumblr blog.

How to Make Your Asks Private in Tumblr - 95