Hi buy photoshop,
<thread moved to the Photoshop forum>
Here's information about finding your serial number: Find your serial number quickly.
If you purchased a Creative Cloud subscription, you'll need a redemption code, as opposed to a serial number. The document referenced above includes instructions for that as well.
Please let us know if you need additional help.
Why I not received a key number by email after I bought Photoshop
If you didn't receive an email from Adobe after you completed your purchase, please check your junk mail folder first. If you don't find the email there, please see http://helpx.adobe.com/x-productkb/global/didn-t-receive-expected-email.html.
Please let us know how it goes.