IMac 3.06 GHz Intel Core 2 Duo
That looks to be from 2008 or 2009.
When you discuss "which Mac you have", the common way to post that is "iMac, xx", early 2008".
I looked at "dosdude1's" page for patches that would permit older Macs to run newer versions of the OS, and he doesn't have anything for Big Sur or Monterey.
4gb of RAM won't be "enough" in any case.
So... my
guess is "no", you can't run those.
You've got a Mac that is just ... too old.
As an alternative...
I'd like to suggest that you consider OS 10.14 (Mojave) instead.
You can find dosdude1's page on it here:
There are instructions and also how you can get Mojave.
If you really want "the latest" (but not necessarily "greatest") OS'es...
... you need more modern Mac hardware.