On current macOS the syntax is changed so substitute
/Volumes/drive_name/Backups.backupdb/mac_name/YYYY-MM-DD-hhmmss for the
<PATH> text at the end of the appropriate command:
sudo tmutil delete -p <PATH>
On Lion and several older OS X, to clean things up properly, delete backups one by one (snapshot by snapshot).
sudo tmutil delete <PATH>
If you are sure you have selected the correct path, you can delete all backups from that one Mac by not passing in the time and letting it delete the entire folder:
sudo tmutil delete -p /Volumes/drive_name/Backups.backupdb/mac_name
The sudo command needs your password (and it won't echo to the screen, so just type it and pause to be sure you're dating the correct files before pressing enter). Also be sure you enable full disk access to Terminal.app or the shell application you choose in System Settings : Privacy & Security
If your trash is already full of "backup files" these commands may not fix the issue and you should copy off any files you need to preserve and then erase the disk. It's usually far faster to do this even if you have to borrow a drive temporarily.