What process are you using. The serial number will not activate the creative cloud version.
If you have purchased the Lightroom 6 Upgrade key you have to download the install package. Run the install package and when prompted to enter key use the LR 6 upgrade 24 digit numeric key first and if you have / had LR 5 or earlier version installed it should be automatically recognized, if not make sure you have it handy when prompted to enter it.
To install the upgrade version of LR6, you need both the LR6 serial number you're given when you pay for the LR6 upgrade as well as a valid serial number for a full version of LR. So if you first bought LR3 as a full version, then LR5 upgrade, then LR6 upgrade, it doesn't want the LR5 upgrade serial number, it wants the LR4 full version serial number.