C it is
For members of the seventeenth-century Ashanti nation in Africa, animal-hide shields with wooden frames were essential items of military equipment, a method to protect warriors against enemy arrows and spears.
Notice that the sentence begins with a prepositional phrase modifying noun clause "Animal Hide shields with wooden frames ". So any verb that describes the action must fit with the prepositional phrase as well.
i.e. for ....(), animal ...() , ???
here for protecting suites the best.
(A) a method to protect
--> this reads for a a method to protect
(B) as a method protecting
--> reads for a method protecting
--- > For protecting sounds right
(D) as a protection of
---> for as a protection of sounds wordy and wrong
(E) to protect
--> for to protect sounds wrong
hope this helps