Michael, there is not enough information here to be useful. "Unit #388" might be a designation for a group of Armed Guard sailors going through training, or it could be a detachment of sailors assigned to a ship for seagoing duty. There were three Armed Guard Centers from which sailors were assigned (in Brooklyn, New Orleans and Treasure Island/San Francisco) so any of the Centers might have had a unit designated #388. It is possible the answer could be found deep in the paper records of the U.S. Navy (now in the possession of the U.S. National Archives and Records Administration) but almost certainly it would not be found, or at least not found easily, online. The Textual Records Division of the National Archives (where paper records would be found) has a blog named "The Text Message." You can submit questions to the blog at https://text-message.blogs.archives.gov/contact-us/. Good luck.
Ron Carlson, Webmaster Armed Guard / Merchant Marine website www.armed-guard.com