The approach is when Odysseus gets the air bags from the keeper of winds and sees Ithaca in sight right before his men open up the bag of bad winds blowing them all the way back to the island of the wind god.
After Odysseus stays with Circe for a year, he breaks himself away and goes into the underworld facing his greates fear and seeing his mother in the underworld. Ths is the point where he hits close to rock bottom.
Odysseus washes up onto the island of Thaecia and is helped by the king who gives him safe passage home.
King Odysseus, disguised as a beggar, approaches his home and finds that it is filled to the brim with dirty suitors attempting to gain his wife's hand in marriage.
Odysseus is furious with the suitors and after the competition, does what none of them could do, string the bow and shoot it through the axes. After this, Odysseus' servants closed the doors and Odysseus and his son began shooting fish in a barrel.
After the death of the suitors, Odysseus goes to claim his wife his is in disbelief that he is Odysseus. Odysseus proves her wrong and proves he is himself by telling his wife about their immovable bed that he made with his hands.