As long as your 2 inch receiver hitch is flush, or close to it, to the back of your 2006 Honda CR-V then the
Thule 914 Roadway hitch bike rack will work great and not be impeded by the Honda CRV rear spare tire. This is a superb fold down hitch bike rack that can hold 4 bikes. I do highly recommend the optional
Thule 955 No Sway cages to ensure the bikes won't swing into each other or the back of your Honda CRV. For security I recommend the
Thule STL2 SnugTite lock to lock the hitch rack to the 2 inch hitch and the
Thule 538 Cable lock to lock the bikes to Thule 914 Roadway bike rack itself. This rack will also work on 1.25" hitches should you ever need to transer the rack over to a vehicle with this size hitch.
The
Thule 912 Roadway hitch bike rack offers the same features as the Thule 914 Roadway bike rack (and the same accessories are available) except that the Thule 912 Roadway is meant for carrying up to 2 bicycles instead of 4.
On a side note since it's such a cool accessory, if you are interested in transporting skis / snowboards during the winter, the
Thule 987XT hitch mount ski & snowboard rack is an excellent attachment for either the Thule 914 Roadway hitch rack or the Thule 912 Roadway.