Multi displays

is the 2011 machine an iMac? If yes, review the document: Use your iMac as a display with target display mode - Apple Support

Target display mode is a feature available with late 2009-Mid 2014 iMacs. The display Mac has to be running macOS High Sierra or older and the signal producing Mac has to be running macOS Catalina (ca. 2019) or earlier.

Your 2011 iMac supports Thunderbolt Target Display Mode. Making a Thunderbolt connection from a modern Mac that has Thunderbolt 3 or 4 ports would be expensive – you would need a $50 Thunderbolt 3-to-2 adapter, plus a roughly-$30 Thunderbolt 1/2 cable. But that's not the issue.

The problem is that Apple added restrictions on the other Mac. That Mac now must have been introduced in 2019 or earlier and must be running macOS Catalina or earlier. Your 2020 iMac fails the model year test. So Apple no longer officially supports using another Mac as a TDM display for the 2020 iMac. It may have been working; it may have been something you expected to have worked – but now that it's officially unsupported, there might have been changes to newer OSes that caused it to stop working.

And even if you reverted to an older OS, there would be no guarantee that it would work!

A 2020 iMac does not support Target Display Mode, if you need an external display please buy one. Please carefully read Target Display Mode

By "Buy One" I mean please buy an external display. There is no such thing as a "target display." External displays are inexpensive and available at an extremely wide variety of sources including your local Walmart, Office Supply store, Costco, Amazon etc..

Help-me-fix-my-Mac wrote:

this was my original situation. I don’t really know what “target display” means:

I have a 2011 21” Mac that I would like to use as a multi display with my 2020 iMac. I connected the 2 with the appropriate cable. It worked for a minute then I couldn’t get it to recognize the Mac again. Can some one please help. Thank you

Target Display Mode (on selected older Macs) meant that you could use them "as if" they were real hardware monitors for other Macs. You had to press a special key combination on the old Mac's keyboard to put it into Target Display Mode, or take it out of Target Display Mode, but that was it.

Macs that supported TDM, and had Mini DisplayPorts, took Mini DisplayPort input. Macs that supported TDM, and had Thunderbolt, needed Thunderbolt input. That was a bit more restrictive in the days in when Windows PCs rarely if ever had Thunderbolt ports. But I can see why there might be a technical reason for it.

Originally there was no limitation on how new the other (signal-producing) Mac could be.

Your 2011 iMac can be repurposed for other work if you so desire, however due to extreme advanced age you may want to consider using Apple's recycling program which is free to you and ensures the computer is recycled responsibly. You can learn about Apple's recycling program by clicking Apple Recycling Programs

A 2020 27" iMac can support up to 2 external displays. Please refer to the technical specifications of your specific Mac. For example on a 2020 27" the technical specifications read:

Video Support and Camera

• 1080p FaceTime HD camera
• Simultaneously supports full native resolution on the built-in display at 1 billion colors and:  
  • One 6016-by-3384 (6K) external display at 60Hz with support for 1 billion colors, or
  • Two 6016-by-3384 (6K) external displays at 60Hz with support for 1 billion colors (requires AMD Radeon Pro 5700 or AMD Radeon Pro 5700 XT), or
  • One 5120‑by‑2880 (5K) external display at 60Hz with support for 1 billion colors, or
  • Two 3840-by-2160 (4K UHD) external displays at 60Hz with support for 1 billion colors, or
  • Two 4096‑by‑2304 (4K) external displays at 60Hz with support for millions of colors
• Thunderbolt 3 digital video output
• Native DisplayPort output over USB‑C
• Thunderbolt 2, HDMI, DVI, and VGA output supported using adapters (sold separately)