Theory:

     The years hurried on, and brought white hairs upon the head of Ernest, and made wrinkles across his forehead and furrows in his cheeks. He was an old man. But not in vain had he grown old; more numerous than the white hairs on his head were the wise thoughts in his mind. And Ernest had ceased to be obscure. Unsought for, undesired, had come the fame which so many seek. He had become famous beyond the limits of the valley. College professors, and even the active men of cities, came from far to see and converse with Ernest, and he received them with gentle sincerity, and spoke freely with them of whatever came uppermost, or lay deepest in his heart or their own. While they talked together, his face would brighten, unawares, and shine upon them, as with a mild evening light.
Explanation:
 
Ernest was a young man known primarily for his hard work and simplicity, and he went unnoticed by his valley neighbours when the story ended in "The Great Stone Face I". On the other hand, Ernest was a well-known figure in "The Great Stone Face II", known to everyone in and around the Great Stone Face Valley.
 
In Part II of Great Stone Face, Ernest had grown up to be a grey-haired old man. The author says he'd gained so much wisdom and knowledge over the years. The author also claims that his wise thoughts outweighed his white hairs.
 
Earnest in his old age.jpg
Ernest in his old age
 
During such an old age, a large number of people travelled from far to meet Ernest. Ernest's reputation had spread well beyond the valley's borders. Despite the fact that he had never sought or desired fame, it came to him on its own. He became a well-known and well-liked figure across the world. Even university professors and men from cities travelled vast distances to interact with such a noble person (Ernest).
 
Those who pay him (Ernest) a visit may expect a warm welcome. When visitors arrive, Ernest would generally stretch his magnificent hands. His age, which is marked by wisdom and experience, allowed him to easily connect with them, expressing heartfelt views. Ernest had established himself as a man of honour, intellect, and simplicity in the valley.
 
Meaning of difficult words:
 
S.No
Words
Meaning
1.
WrinklesLines on the skin when you grow older
2.
Furrows A deep line on the surface of something
3.
NumerousSomething that exists in large numbers
4.
Ceased To stop something from happening
5.
ObscureAn unknown thing
6.
UnsoughtNot searched for
7.
IntegrityBeing honest and having moral qualities
Reference:
National Council of Educational Research and Training (2008). Honeydew. The Great Stone Face II - Nathaniel Hawthorne (pp. 128-132). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.