To close a ticket, first you should navigate to the ticket – Navigate to your ticket.

There are two ways to close a ticket:

Close a ticket without issuing a reply

In the ticket details metabox on the right side of the screen there is a small link called Close.  Just click it and the ticket will update to closed.

The image below show where in the metabox the link is located – see the red box.

Close a ticket with a reply

At the very bottom of the ticket is the reply area.  Fill out your reply and then click the REPLY & CLOSE button.

The image below shows the location of this button in the reply area: