Error when upgrading to vs 4.6.8
That table is involved in reminders, and was introduced in CiviCRM 3.4, so there is a serious issue with your database. I recommend restoring a backup of your site and database (you have those, right?) and trying the upgrade again. Please note the first errors you get, as those are often most useful in diagnosing what is going wrong, rather than later more serious messages.

It would likely be a good idea to verify that the table is in your backup before starting the upgrade.