As of recent years, Adobe has removed these links and non-activation serial numbers from their public site.
For users who require additional assistance or support, here are some additional resources: Adobe Acrobat 8 Professional Serial Number Activation Code
The primary hurdle for users today is that Adobe retired the activation servers for Acrobat 8 (and other Creative Suite 3 products) years ago. Because the software must "call home" to verify a license, and the server it tries to reach no longer exists, even a valid, legal serial number will often result in a connection error. Can You Still Use a Serial Number? As of recent years, Adobe has removed these
Adobe now considers Acrobat 8 "dead and gone." They do not provide new codes, and they recommend that users move to modern, supported versions for security reasons. Risks of Using "Free" Serial Numbers Online Can You Still Use a Serial Number