iMac Big Sur 11.4 doesn't connect to projector ..

What year model iMac?

see > Identify your iMac model - Apple Support

What projector?

(make, model, input connections)

To connect an HDMI equipped Display, TV or Projector to the newest iMac's, you will need a USB-C to HDMI adapter.

For example Apple sells the > USB-C Digital AV Multiport Adapter - Apple and > Belkin USB-C to HDMI Adapter - Apple

For more info on connecting displays to an iMac, see > Connect an external display to your iMac - Apple Support