Updated Mac Os to bigsur and my CS4 doesnt work. I tried downloading and reinstalling does not work

CS4 is legacy software from 2008.  You need modern software that's compatible with new  operating systems.  Keep your old computer to run legacy CS4 & never upgrade it.  

MODERN OPTIONS:
Photoshop Elements (approx $100, no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Camera Raw
• Lightroom on desktop, mobile and the web
• Lightroom Classic
• Portfolio website + hosting
• Adobe Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).
• Free upgrades for paid subscribers

https://www.adobe.com/creativecloud/photography.html

Premium Adobe Express ($10/month).

• Creative Cloud Express app (web and mobile)
• Premiere Rush (desktop and mobile)
• Photoshop Express (mobile)
• Spark Video (mobile)
• Spark Page (mobile)
• Adobe Portfolio + hosting
• 100 GB of cloud storage
• All premium templates and design assets including the collection of over 160 million royalty-free Adobe Stock photo collection.

https://helpx.adobe.com/express/using/express-overview.html

Creative Cloud All Apps (51 + apps & services) and Single App Plans
https://www.adobe.com/creativecloud/plans.html

Make sure your computer meets the minimum CPU & GPU requirements. Most Creative Cloud apps work on:

• Windows 11 (64-bit), Windows 10 versions 21H2, 21H1, 20H2, 2004, and 1909 (LTSB branches are not supported;)
• macOS 12 (Monterey), macOS 11 (Big Sur), macOS 10.16 or 10.15 (Catalina).

- https://helpx.adobe.com/creative-cloud/system-requirements.html
- https://helpx.adobe.com/photoshop/system-requirements.html
- https://helpx.adobe.com/photoshop/kb/photoshop-cc-gpu-card-faq.html

Hope that helps.

Then i deleted it from my folder and when i download the new photoshop, i double click on installer and it doesnt do anything?

By @Max2676505912c2

 You can't just delete folders, you have to uninstall.

I suggest that you use the Cleaner Tool, restart the computer, and then try installing compatible programs.

https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

big sur is not compatible with cs4.  there's no work-around for using cs4 with any 64 bit-only os like big sur.

you can use an older os, or use more recent adobe programs that are compatible with big sur.

if you have an adobe subscription, you have access to compatible apps in your plan.  why don't you use them?

Let me move this to the Download & Install forum for you, which is the appropriate forum for your question.

* The Using the Community forum is for help in using the Adobe Support Community forums, not for help with specific programs, installation issues, or account issues such as subscription questions or billing problems, or generalized questions about Creative Cloud services.
* Questions about business plans should be posted in Enterprise and Teams 
* Product questions should be posted in the associated product community.
* Installation questions should be posted in the Download & Install community.
* Account issues, including subscription questions or billing problems, should be posted in the Account, Payment, & Plan community.
* Questions about the Creative Cloud desktop app or general questions about apps in the Creative Cloud should be posted to the Creative Cloud Services community.