Relocate catalog and image files from my desk top to an external hard drive.

This is a common requirement and the solution is the same as moving your catalog and photo files to a new computer.

https://helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html

There is another way, which is to use the ability of the left folders panell to move whole photo folder trees from one drive to another by drag and drop. That's fine if you want to move selectively a part of your folder tree to another drive. However, since that very important change in your computer deserves a backup before it is performed, you don't save much time compared with the recommended backup and restore process above.

At the end of the restore, the catalog folder is also moved in 'custom' location under the master folder you have chosen for the move. You can move it back to the default location or nearly anywhere else since its contents stay the same.