Here's a walkthrough on installing the license for SketchUp Pro, the actual process of installing is fairly straight forward.
Add Classic License
instead.serial_number : WH-00161147-CER
auth_code : ad341e9f841406
From here, you should be able to launch into SketchUp!
Check that you are entering the license codes into the correct version of SketchUp Pro. For example, if you purchased Sketchup Pro 2021, the license codes will not work in Sketchup Pro 2020.
Make sure you completely uninstall all previous or trial versions of SketchUp and SketchUp Pro before installing. You must have old empty SketchUp folders deleted and software properly uninstalled and restart your machine before you begin.