As long as you have at least a Class III 2 inch hitch on your 2008 Honda Odyssey EX-L, you will be able to use the Thule Transporter Hitch Mounted Cargo Carrier, part # TH665C.
The Thule Transporter tilts down to allow access to the hatch on your Odyssey. You will also want to measure from the center of the hitch pin hole on the vehicle out to the distance needed to clear the rear bumper. If that distance is less than 7-1/2 inches the carrier will clear the rear of the vehicle.
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