To close a ticket, first you should navigate to the 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: