How to Install latest mac os catalina, to the older laptop
Download the latest version of the Catalina patch here. Open the Catalina Patcher app.
Click Continue.
Choose Download a Copy.
The download (of Catalina) will start - since it's almost 8GB it is likely to take a while.
Plug in a flash drive.
Choose 'Create a bootable installer' from the options.
Plug the bootable installer into the Mac you wish to update.
Restart the Mac while holding the Option/Alt key. This will cause the Mac open in Startup Manager.
Choose the bootable installer drive and Enter.
Now your Mac should open in Recovery.
Choose Reinstall macOS and wait for the new version of macOS to install.
After the installation has completed, you should restart the Mac in Recovery mode again, choosing the drive that contains the bootable installer.
Now choose macOS Post Install and the required patches will be installed on your Mac so that Catalina can work.
When the patches have been applied to choose Force Cache Rebuild.
Restart.


I also suggest you go through this video.