I have updated my Lightroom Classic to version v 12-4 but the old version opens

What old version? Lightroom Classic 12.3? That would mean the update failed. The old Lightroom 6 that you did not remove? 

Do you have restart your computer?

Another step is to try to reset the Lightroom preferences.

https://www.lightroomqueen.com/how-do-i-reset-lightrooms-preferences/

It's recommended to backup your preferences before you reset the preferences to the default settings:

https://helpx.adobe.com/lightroom-classic/kb/preference-file-and-other-file-locations.html

If this doesn't help we need more informations about your environment.

Please provide also a copy of your 'System Info'. This can be get from the LrC Help > System Info menu item.

There's a copy button in the System Info dialog. Press this button and paste the info into your next forum post.

You can also try to do a clean reinstallation of Lightroom.

Please follow the steps below:

• backup all personal data, like templates, presets, catalog(s) etc.
• uninstall everything cc including preferences,  https://helpx.adobe.com/creative-cloud/help/uninstall-remove-app.html
• then uninstall the cc desktop app,  https://helpx.adobe.com/creative-cloud/help/uninstall-creative-cloud-desktop-app.html
• clean your computer of cc files per http://www.adobe.com/support/contact/cscleanertool.html
• restart your computer (don't skip this)
• reinstall the cc desktop app,  https://www.adobe.com/creativecloud/desktop-app.html
• use the desktop app to install your cc programs/trials
• restore your personal data.

if you're unable to install the cc desktop app at this stage, use an administrator account (solution 4 here,  https://helpx.adobe.com/creative-cloud/kb/creative-cloud-missing-damaged.html)