Log into your Magix account- once registered it is stored there. They inherited the database from Sony. All legitimate sellers provide a serial number so you can contact your retailer.
Anyway, 8 is very old at this point so if you have a recent computer I'd suggest purchasing Vegas Edit 19 or one of the monthly subscriptions instead.
The OP may not have it migrated to the MAGIX account. If he/she bought and registered it during the "Sony/SCS era", the serial number might be found at https://www.sonycreativesoftware.com/myaccount/mysoftware assuming the login details are still known. Probably the case is not that though.