Laurie, if Basecamp is the Garmin application you are using, that should be able to make the move. It should also be possible to do this from the operating system by copying the files to a new location and renaming them so that the Garmin thinks they are active tracks. That second option will allow you to do this on a computer that does not have the Basecamp application loaded, but it has a strong geeky language warning.
The Basecamp approach is simple, but before you connect your GPS unit, take a note of the names of the archive tracks that you want to reactivate. They will appear on the device in a form like '2015-09-23 06:56:12' unless you have changed the default name offered when you archived the track.
When you connect your GPS, and its information appears in the Basecamp side panel, then
- select the first track you want to reactivate. Note that it should be the name you have already copied with a word like 'Day', 'Stopwatch' or 'Auto' at the end.
- open the context menu (alt-mouse button, normally right mouse button)
- click on the option 'Create Route from Selected Track'. A menu box will open.
- either leave the number of points to be selected automatically or enter a number, and press the 'OK' button.
- this will create a route. If you now want that to be a track that you can use, then
- select the route you have just created
- open the context menu
- click on the option 'Create Track from Selected Route'
- the new track should appear.
Repeat for all the archived tracks you want to re-activate.
If you want the instructions for doing it from the operating system, let me know. I can explain how to do it in a Microsoft Windows environment (not Apple or Android).