For the boxed product the serial number would on on the disk sleeve or the in the box on a card.
If you do not have this you could try logging into your account at magix.com with the email address and password used to register the software when it was first installed (if you had to do this) and under My Products there you should find your serial number.
Web Designer Premium 10 is now a rather old product so whether it will run fully under any relatively modern OS is something you may need to consider.
However, to access your serial number and assuming you originally registered your purchase of the software, go to your Magix account, log in, go to My products and find the listing for your software. The serial key will be listed there.
You might also care to check how many activations are currently listed for the software, and deactivate any and all you no longer need. That will prevent any problem of the Magix servers refusing to allow you to register your new installation because you have exceeded the maximum number of installations you are allowed.
If you cannot log in to your account for any reason, or if the information about your software is not listed in your account you will need to email infoservice@magix.net with as much information as you can give them and ask for them to send you your key.