In a strange region he scales steep slopes;
far from his friends he cuts a lonely figure.
Where he bridges a brook or wades through a waterway
it’s no surprise to find that he faces a foe
so foul or fierce he is bound to use force.
So momentous are his travels among the mountains
to tell just a tenth would be a tall order.

Although he is in his final leg of the journey to the castle where he stays until the day he travels to the Green Knight's castle, he doesn't know this yet. On the mountain that he encounters, he has some trouble and it takes him quite a long amount of time to be able to make it up the mountain. He has to deal with many problems including snarling wolves, bulls, hears, wild boars, and the mountain winter, in which he almost froze to death many times, especially in his sleep.
This exerpt displays the lengths that Sir Gawain is willing to go to honor his word almost a year earlier.