I don't know how to resolve this .

Question

I have taken advice about backing up my mac, but this always happens , where am I going wrong ... It's new and has 999.86 Gb free.

Answer 1

The backup volume was full. That shouldn't happen, because TM is supposed to manage disk space by deleting snapshots as needed to make room for a new one, up to the last complete snapshot, which is never removed automatically. Normally, a snapshot won't be started if there isn't enough space for it.
First, I strongly suggest that you start a new backup (not necessarily with Time Machine) on another external drive. A single backup isn't enough to be safe.
One possibility is that you were writing other data to the volume during the backup. Apple recommends that no other data be stored on a backup volume. If two or more computers back up to the same volume over a network, they will compete with each other for space.
If you've moved any files to the Trash on the backup volume, empty the Trash.
Sometimes a restart will clear the error.
Reports suggest that the error may sometimes be caused by a bug that's triggered when you don't use a backup volume for a long time, perhaps two weeks or more. If that's the case, ask for further guidance. You may have to erase the backup volume to work around the bug.
Otherwise, turn Time Machine OFF temporarily in its preference pane. Launch Disk Utility, select the backup volume, and run Repair Disk. That operation may take a few hours. If the volume is repaired successfully, or if no problems are found, try another backup.
Disk Utility may be unable to repair the volume. In that case, you should stop using the drive and put it aside until you're sure you'll no longer need the data on it. Then erase it and start over, or (preferably) replace it.
If TM still isn't working right, start up in Recovery mode and repair the startup volume ("Macintosh HD," unless you gave it a different name) the same way. Restart as usual and try TM again.