I cannot install Monterey- not enough disc space on Mac Big Sur

Are you asking how to increase your disk space so you can install Monterey? If so, I would recommend buying an external HD such as a OWC Mercury Elite Pro and moving your large libraries such as your:

• Photos library
• Movie library
• Music library

to the External Hard Disk, then put the libraries that are stored on the internal HD in the Trash and Empty the Trash. That should free up quite a bit of HD space so you have adequate space. If you do not know how please read Apple's instructions in Move your Photos library to save space on your Mac

The files that you have control over are located in the Documents, Downloads, Pictures, Music and Movies folders.  You can use either of these two free apps, GrandPerspective  or OmniDiscSweeper, to find the largest files on your drive so you can determine if they can be deleted or moved to an external HD for storage.  

Note: you can empty the Downloads folder after the apps and/or updates that were downloaded have been installed or applied.  Many users have found a couple of Gigabytes of files in their Downloads folder which are no longer needed. 

You should strive to maintain a minimum of 50 GB of free space at all times, more if possible, to facilitate optimal system and application performance.

As for an external hard drive you would be better served with one of OWC's portable SSD:

I recommend drives from OWC (MacSales.com) as they have proven reliability, excellent customer support and warranties.  Consider one of these depending on your budget and needs:

OWC ENVOY PRO ELEKTRON

However, for your model contact OWC's customer support and get their recommendation for the SSD model that would best suit your iMac model, needs and budget.  They have additional models other than the one I've linked to above.

It's not memory you don't have enough of, it's storage. And the answer is the same I gave rtoruno.

I don't have enough memory to install Monterey?