Final answer:
The Green Knight's proposal to Sir Gawain is a beheading game where Gawain has the opportunity to strike The Green Knight, with the perilous catch being that he must receive a similar blow in a year and a day.
Step-by-step explanation:
The proposal mentioned in the story relates to the character The Green Knight, who challenges Gawain to a beheading game. The terms of the challenge are peculiar and dangerous. The Green Knight offers to allow anyone to strike him with his own axe on the condition that he gets to return the blow in exactly one year and one day.
Sir Gawain, a knight of the Round Table, accepts the challenge. He beheads The Green Knight, who then astonishingly picks up his own head and reminds Gawain of the promise to receive a similar blow in a year and a day.
The other options listed in the question, such as King Arthur offering his kingdom, Sir Bertilak offering a magical sword, or Morgan le Fay offering invincibility, are not accurate to the source material.
The Arthurian legends, which include characters like Sir Gawain, Sir Lancelot, and the tales of Camelot, often revolve around chivalry, honor, and mystical challenges, as is evident in this beheading game proposed by The Green Knight.