In the clone (which has already been suggested and a very wise one at that), Server - Environment - Update Component.
The pick list of which Moodle version to check should now have higher versions. Check each and note the changes to not only Moodle version, but PHP version, MySQL version, DB config, etc.
It will help map out strategy for what to do when along the march to latest and greatest.
PHP version ... for example ... cannot upgrade PHP to 7.0.x or higher until one gets to 3.0.highest. So the 2.6 -> 2.9 hops (note that is plural depending upon your preferences in hyperjumping nor not) will have to be performed using your current php version.
Also make sure, in the clone march, backup code and DB after each successful step up in the march. IF a step hickups, you might have to restore the previous step/upgrade.
'spirit of sharing', Ken