If it is the second time that you will be activating it then you just need to log in to your adobe.com account & go to your orders & reinstall then activate it just like you did in your first computer.
It is the third or more than second activation, then
When you install it on the third computer or for the third time & when you to activate it, if it installed & activated already twice, there will be an option of deactivating it from the previous computers, please click on that.(To deactivate from pre-installed machine, Open any Adobe CC application > Help Menu > Sign out.)
Next it will allow you to activate on your new machine,
Now you can go back to your first computer, log out & log back in of Desktopp CC App, launch any product, if there is any product to buy, in that prompt there will be an option to " license the software", please click on that & sign in.
It will reactivate the CC on the first machine.
You have already deactivated it from one machine, hence you can activate it on third computer.
In case the is still not resolved, please contact Adobe at
Regards
Rajshree