The VEGAS Movie Studio 15 Suite is perpetual (i.e. one-time purchase) only, not a 365 subscription. So two simultaneous activations allowed for you. (Note that some 3rd party plugins in the Suite may allow only one activation.)
If you are having trouble activating go into your Magix account https://www.magix.com/us/support/my-service-center/ Look at My Products and check the activation slots for your VMS15. It may be that your current installation is showing in both slots. If so deactivate one so it is free for activation from your second machine.
@Kyle-Burson Usually when you uninstall it automatically deactivates itself. But that depends on there being an internet connection. Possibly at the time you uninstalled it couldn't get through to the Magix servers as there have been server problems recently.