In what part of "The Odyssey" does it say why Penelope has waited so long to pick a new husband?Please include a quote that says why she waited.
You wouldn't have half of the book if she didn't. Just kidding. Here is a quote that in a round about way answers your question...it comes from book 2, page 2:
"If I can hear of him as alive and on his way home I will put up with the waste you suitors will make for yet another twelve months. If on the other hand I hear of his death, I will return at once, celebrate his funeral rites with all due pomp, build a barrow to his memory, and make my mother marry again.”
In essence, even though he has been gone for so many years, Penelope still holds out hope that Odysseus is not dead. For that reason she doesn't want to choose a new husband. But this goes against what most people seem to consider reasonable. After such an absence, the men feel that it is only right that Penelope chooses a replacement husband and they are determined to hang around until she does so. She does not have the strength of personality to get rid of them, and her son does not have the physical strength to chase them out. Thus, they are stuck with the pigs eating them out of house and home.