My Time Machine is taking days to back up this Mac... and using more memory that the computer has stored. This used to be a small file with tons of backups. I can't even get one back up on this 4tb hard drive.

TM Backup uses disk space to store the data set not RAM.

How old is the hard drive? If five or more years old it should be replaced. If giving problems now it should be at least erased and re-established as a backup drive if not replaced. You apparently have already reformatted to no avail.

I suggest you get a new HDD and set it up and obviously retest. HDDs are too cheap and life's too short to worry about a hard drive and its continued operation.

How full is your internal drive? You need to check that and make sure 15-20% of it is totally unused all the time. This facilitates the smooth and error free operation of the entire system.

The size of the TM data set will depend on how much data you have on the internal drive. Since TM no longer backs up the OS, that will be on the order of the total disk usage less somewhere around 20GB for the initial backup. But, over time the TM dataset will grow as you add data, apps and such to the main drive.

Again, but, each successive backup adds only the changes so that should happen much much faster. If it's not the initial backup and it's taking so long, something is definitely wrong. I suggest you halt the process and try that new HDD as suggested.

I couldn't add this edit earlier.

You state you have a 4TB backup drive. Your screen shot shows 3.06 TB copied which is listed as 52%. If those numbers are correct, there is no way you'll ever get 6TB of data on a 4TB drive.