After buying of new PC Adobe CS6 doesn't recognise that it is registered and not allow to use my key

When you can't deactivate a serial number
BE SURE TO ONLY ASK FOR ACTIVATION SUPPORT TO ADJUST YOUR ACTIVATION COUNT
You may need to PERSIST or TRY AGAIN to find a support agent with more experience

Be sure to remain signed in with your Adobe ID before accessing the link below
Do be aware that Adobe's staffing is impacted by the virus, so wait times are long
-make sure that your browser does NOT block ads, scripts, or pop-ups
-you must also allow 'cookies' in your web browser for this to work
https://helpx.adobe.com/contact.html?rghtup=autoOpen
.
Also: beware of answering anyone who sends you a private message
-click for more information about scammers https://tinyurl.com/10791730

A lot of apps used to work this way (a little less today). The license is tied to an activation on one machine, and "machine" is worked out from a combination of all sorts of things like CPU, disk serial numbers, and secret sauce. This is to stop someone walking up to your machine, taking a clone of the disk, and getting your software. But it's a pain when doing any kind of system recovery.  This was fixed around 2014 when Adobe went to subscriptions, which now rely on having an internet connection and being signed in. But if you want to run this ancient (but excellent) software you've got to play this game.  Now, you were limited to two activations before needing to contact Adobe. If it says, specifically, "activation count exceeded" you need to contact Adobe to have an "activation count reset" - ask for that exact thing, don't paraphrase, don't start with discussing anything else. If the message isn't "activation count reset" that isn't the issue.

You will have to reinstall. The "elsewhere" is the old computer, this is recognised as a new one. If you can get the old PC working you can Deactivate the apps. Otherwise you need to ask Adobe to do it. Warning, scammers may contact you privately pretending to be Adobe staff. Adobe will never send you a private message asking you to email an account that isn't @17309390, or use Skype. Adobe never ask you for their password. These scammers want your Adobe info, credit cards, your money and control of your computer, please take care.