You can have creative cloud installed and signed in on two computer (mac, pc, or both), as long as you only use it on one at a time. Download and install as you did on the first computer, sign in to your Adobe account on the Adobe website using your Adobe ID, download the Cloud desktop app, then download the software.
You can download the installer for Creative Cloud from here :
Creative Cloud Help | Creative Cloud for desktop.
After you install the Creative Cloud desktop application , you will need to sign in with an Adobe ID and Password. Then you can install apps. This link offers more information and step by step instructions if you need it: Creative Cloud Help | Download, install, update, or uninstall apps.
If you are talking about purchased (perpetual) software, you can install and activate (purchased) perpetual software two computers of the same type (mac or pc), as long as you only use it on one at a time. (lightroom is the exception as it is a multi platform product, so it can be installed on pc and mac platforms)
It is a good practice to deactivate software on a computer where it will no longer be used, especially before giving away or selling the computer, or reformatting the hard disk. Please see this link: how to deactivate software. This frees up one activation so you have the option to install the software on another computer at any time.
If you don't have access to your previous computer because you replaced a hard drive, upgraded your operating system, formatted your computer before deactivating your software, or your computer died, you can ask Adobe Support to help you deactivate from a machine you cannot access. Have your serial number or Adobe ID ready, and then contact us.
This software is for one platform or the other (except multi platform Lightroom versions). Only CS6 can qualify for a platform swap.
See this link:
(For version CS6 only, a platform swap is available from mac to pc or pc to mac):
If you change operating systems or require a different language version of a product, you can order a product swap, or crossgrade. You can swap to the current version of a product—for example, Creative Suite 6—and to an available language version. This page provides instructions on these actions.
Note: If you have an older version of a product, you must order an upgrade instead of a swap. Place upgrade orders directly with Adobe Sales. (Visit your region's Adobe Store for contact information.
I hope that helps.
Thank you very much for the reply and your detailed guideline.
You are very welcome.