Hi!
When I want to creat a backup this message appear
"error/cannot_create_backup_temp_dir"
Since you've not mentioned details concerning your server/setup, the following is general ... from the / in the error assume it's either Linux or MacOSX, but the following would apply.
Check the permissions on your moodledata folder. It must be readable and writable by the web server user underwhich apache/IIS runs. If your server were Linux and CentOS, as an example, the root user could
chown apache:apache moodledata -R
and
chmod ug+rw moodledata -R
When backing up, Moodle uses moodledata/temp/backup as it's work area.
'spirit of sharing', Ken
Use moodle.org's site search before posting questions, please. I immediately found this thread with your same error message.