Final answer:
In the story of the Odyssey, Penelope avoids picking a new husband by weaving a burial shroud for her father-in-law and unraveling it each night. She also sets up a challenge for her suitors that none of them can meet.
Step-by-step explanation:
Penelope repeatedly avoids picking a new husband through various means in the story of the Odyssey. One of the ways she avoids marriage is by weaving a burial shroud for her father-in-law, Laertes, and promising to choose a new husband once it's complete. However, she unravels her weaving every night, delaying the completion of the shroud. This strategy buys her more time and prevents her from having to choose a new husband. Another way Penelope avoids picking a new husband is by setting up a challenge for her suitors. She tells them that she will choose a husband based on his ability to string and shoot an arrow through a row of axe heads. By raising the bar for potential suitors, Penelope ensures that none of them are able to meet the challenge and thus she does not have to choose a new husband.