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Derailleur hanger is a metal extension of the rear dropout through which a rear derailleur is mounted. If the rear derailleur is damaged, mostly likely the derailleur hanger could be damaged as well and has to be replaced. It's also recommended to carry a spare derailleur hanger when riding a mountain bike.
Below is a reference of compatibility list. On top of that, please always compare the geometry of your original derailleur hanger with that in the picture to make sure you are purchasing the right part.