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Adobe Photoshop Elements is an older version, but you should still be able to retrieve your serial number if you obtained or registered your software with Adobe. You should be able to log onto your account at https://accounts.adobe.com
Once you log in, select the icon titled "Plans and Products" and see if your software license is there. If it is not, you may need to contact an Adobe representative at https://helpx.adobe.com/contact.html?step=ZNA_downloading-installing-setting-up_serial-numbers-redemption-codes_stillNeedHelp#