What are three instances from book 12 of the Odyssey that proves Odysseus is being a hero?
There are many instances throughout The Odyssey where Odysseus acts heroically. A hero, according to Cambridge Dictionaries Online, is "a person admired for bravery, great achievements, or good qualities." In Book 12, we can find three such examples of Odysseus acting as a hero.
The first example of Odysseus being a hero is when he and his men face the Sirens. Circe told Odysseus that he must be the only one to listen to the Sirens, so Odysseus melts wax for all the men to plug their ears, and then he orders his men to tie him up to the mast and not release him under any circumstances until they are safely past the Sirens. This is heroic because Odysseus acts bravely; the Sirens tempt Odysseus to go to them and leave his ship and it is far from easy to resist, even while tied, but he does.
A second example where Odysseus acts as a hero is when he boosts the morale of his men throughout the difficulties they face on the ship. Odysseus "went through the ship, cheering up the crew, standing beside each man and speaking words of reassurance." This is heroic because Odysseus cares for his crew, not just himself, and it is far from easy to be a leader, but Odysseus successfully leads his men. It is an example of a good quality, as we see in the definition above.
A third example of Odysseus as a hero in Book 12 is when he survives, even after all his men are killed. The men angered the gods when they killed and ate the cattle of Helios, and after they set sail, their ship is attacked. He makes it once again through Scylla and Charybdis and then floats for nine days until he reaches land. The fact that he survives on his own for so long and through such perils is a great achievement and therefore certainly heroic, according to our definition above. (Also, it is important to note that Odysseus tried to warn his men and told them not to eat the cattle, but the men did not listen, so it is not Odysseus' fault when they die because of the wrath of the gods.)