In your sentence "Hand me the hammer",Hand definitely is not a noun. It is a verb (used with object) defined as: to deliver or pass with as if with the hand ,to help,assist or guide.
The underlined word in the given sentence is "hand". The word "hand" as used in the sentence is a verb. The correct answer would be option A. It is used as a verb because it means to pass, to give to or to pick something up.
