Final answer:
In "The Odyssey," Penelope says that the completed task which will determine who becomes her future husband is stringing and firing Odysseus' bow.
Step-by-step explanation:
In "The Odyssey," Penelope says that the completed task which will determine who becomes her future husband is C) Stringing and firing Odysseus' bow. In Book 21, Penelope announces that she will marry the man who can string Odysseus' bow and shoot an arrow through twelve axe handles. This task is significant because only Odysseus himself - the rightful husband - is able to accomplish it.