3
The wooers had been in Odysseus palace for 3 years
3
3
By the time her son went out to find his father Odysseus, she had been putting of the wooers for three, almost four years.
3 years
Because she didn't know if it was actually him, people came to her all the time with lies about Odysseus
3 years
The suitors were challenged to string Odysseus' bow and then shoot an arrow through 12 axes. None of the suitors are able to accomplish this; the bow of Odysseus had never been strung by anyone besides him. An old man was able to accomplish it; however it was later revealed that the old man was Odysseus in disguise.
Odysseus stays with Calypso [The Hider] on Ogygia for seven years.
Odysseus was away from his home 20 years
yes
Odysseus was in Troy when he was away from Ithaca for 20 years. He was away from Troy for 10 years, and never revealed where he was at during that time.
Odysseus has been away from his palace at Ithaca for eighteen years (nine years in the war, nine years attempting to sail home). During this time he has been presumed dead, and he finds his palace full of local minor lords - all attempting to marry his widow Penelope (who probably has substantial property in her own name). Odysseus realises that his only chance of getting rid of all these leeches (who will gang up and kill him if they realise he is the returning Odysseus) is to get himself into his house in disguise and pick up his old bow from the armoury. Since Odysseus' life depends on staying incognito, he must be careful who he identifies himself to. He lets his son Telemachus know who he is - because when the fighting stars, he will need Telemachus' help. Eurycleia was his nurse when he was growing up; it would be very difficult to stop her from realising who he is.
because he has been gone for twenty years