I'm hoping that the menus on your Nav6 are similar to this from a Nuvi 56:-
Fig 1 - Select Trip Planner
Fig 2 - Select an Existing Route (Home Work Trip)
Fig 3 - 'Map' displays Route (travelling from left to right)
Fig 4 - from Fig 2 select 3 lines (top left) for 'Edit Trip' >> 'Edit Destinations'
Fig 5 - Touch and drag top yellow arrow down to swap two entries >> Save
Fig 6 - Go back to display re-ordered trip
Fig 7 - 'Map' now shows new route (from Right to left)
If it is not possible to reverse the Route on the Nav6, you can reverse the Route in Basecamp before downloading it to the unit with :-
Right click on an existing Route under 'My Collection' >> Select Invert Route