Photoshop version conflict - CS6/CS3

I recently bought a licensed copy of Photoshop CS6

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Adobe hasn't sold CS6 since Jan 2017.  So you either bought pirated software or you're using a used version from an auction site.  Unless you and the seller completed an official transfer of license form to Adobe, I'm afraid you don't even own the license to whatever it is you purchased.

https://helpx.adobe.com/x-productkb/policy-pricing/transfer-product-license.html

Sorry to say, this sounds like a scam.  I hope for your sake it doesn't contain malware.

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Beware of fake Adobe reps who may contact you privately offering to sell you software or take control of your computer. It's a scam, run away! Real Adobe employees will never reach out via Outlook, Yahoo, Gmail or Skype.
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Personally I'd be wary of uninstalling. CS3 will never work again, and CS6 may not install on current systems. It's many years obsolete, not sure it was a good investment.

Best to just give up on double click to open and use the safe way (File > Open in the app).

Hi Andrei!

Try removing both CS3 and CS6 with the 'Creative Cloud Cleaner tool':

• https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

If the tool did it successfully, close it and restart your PC and install CS6 again.