There's lots of ways to change the ticket status. The administrative user can EDIT the ticket and change the status manually and save. I could have created a select list using taxonomy terms and used that to trigger status change. What I've done instead here is ask RULES to check to see if a certain text string appears anywhere in comment section--in particular, "close ticket."
If "close ticket" appears in the comment section, when a new comment it saved, it changes the status from Active to Closed. Any new comment from Admin or the user will cause the ticket status to change back to "Active."
One of the things you can learn from this example is how to set up a series of OR conditions after a set of AND conditions. I have found the logic of these conditions difficult to create. What you see below would read: If this is true AND if that is true, AND if any of the following under the OR header are true, then the condition validates as true.