Facebook users can post what’s going on in their lives in a very public way on other users’ pages. If you don’t want everyone to read your musings, you can send a private message to a friend’s Facebook in-box. This feature is a convenience that can be safer than sharing your own personal email address or personal information online. Like any email client, you can keep Facebook email after you’ve read it, or choose to delete it from your account. But with Facebook, the email is irretrievable after you delete it.
Log in to Facebook.
Click the “Home” tab, which is located on the right-hand side menu bar.
Click “Messages” on the left side of the page under your Profile picture.
Click the specific email or email conversation you want to delete. Click the “Action” drop-down menu, then select “Delete Messages.” Click “Delete All” at the bottom of the Facebook page to delete all the emails in your in-box, or check the box next to an individual message, then click “Delete Selected.” Facebook will permanently delete the messages from your account.