You would use "he" here because at a later part we encounter "he can graduate" which shows that the doer of the action is a male and therefore requires "he" to be used.
He Green Knight<span> says that he will allow whomever </span>accepts<span> the </span>challenge<span> to strike him with his own axe, on the condition that the challenger find him in exactly one year to receive a blow in return. ... As soon as Arthur grips the </span>Green Knight's<span> axe, Sir</span>Gawain<span> leaps up and asks to </span>take<span> the </span>challenge<span> himself.</span>
I think that it is the strength of hope.
May I ask what the questions are?