I am trying to back up, i was under the impression the old back ups would delete. However my external HDD is saying there is not enough room.

Sorry for my units-confusion. I seem to get the units wrong a lot.

The computer I learned programming on had 4K of RAM, and "mass storage" was paper tape.

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your drive does not appear to be big enough for the way you use your computer.

You can ADD an additional drive at any time, and Time machine will start a new stand-alone backup set on the new drive. Then the old drive can be removed at any time.

How large is the backup drive in total?

For long-term trouble-free operation, recommended drive size is at least 2.5 times the size of what needs to be saved, or larger.

Because time machine does its work in the background at low priority, the backup drive does not benefit from being FAST.

Then I think you will need a larger drive in the long run. It will be very difficult for Time machine to shoehorn an additional 426GB onto a drive with another backup of about that size already in place on that drive.

You could erase the drive and do a fresh backup, but you will be "working without a net" until the new backup completes, and then in a few days, you might be facing the same issue again.

¿did you leave the drive disconnected for a long time? Usually if Time machine can backup small pieces frequently, it does not run into a 426MB roadblock.

Recommended drive size is at least 2.5 times the size of what needs to be saved, or larger. That gives long term trouble-free operation (set and forget).

Oops, I forgot to mention:

When multiple drives are available, Time machine will normally alternate backups: Every-other backup goes to every-other drive.

That may or may not happen in your case, where the backups to the smaller drive are "stuck".