I hope that you have authorized ADE on your work computer with an explicit Adobe ID?
If so, authorize your personal computer with the same ID.
You may need to deauthorize it first, ctrl-shift-D (cmd-shift-D on mac) in library view.
Doing that will lose access to any books under the ID the home computer was using.
If you haven't authorized the work computer, see below.
This is a vicious trap that Adobe lays for unsuspecting customers.
They do give very mild warnings, but not nearly strong enough.
When you register 'without ID', ADE creates an anonymous/implicit ID with limited powers (eg can't be used to share with other devices).
Whenever you first load a DRM book, that copy of the book is associated with whatever ID the computer is registered to at the time.
Any book you load while this anonymous ID is active gets associated with that ID, and can't be read on any other device.
When you properly register your computer with a real ID, that old anonymous ID is lost.
Now you don't have any devices that can read the book.
The only way I know round this is to use a DRM stripper such as epubee BEFORE you deauthorize the device.
I do NOT advocate using such code to get around the valid limitations placed on a DRM book.
However, where the problem arises only because of the ineptness of Adobe's ADEPT DRM infrastructure and its implementation,
such a measure is totally justifiable.