Robert Walton is 28:

Now I am twenty-eight and am in reality more illiterate than many schoolboys of fifteen.

We learn that Walton feels "illiterate" because he was home schooled or "self-educated" and therefore has gaps in his education. He also tells his sister in his letter that he is lonely and longs for a friend. We find out that he has spent the last six years preparing to become an arctic explorer. He now has a ship that he will sail to uncharted places.

Walton explains that he could have lived in ease and luxury but has preferred to pursue the "glory" of exploration. He knows his path will be difficult and will take fortitude, and he wishes he had someone to help him along on his journey.

All of this background helps prepare us for his encounter with Victor Frankenstein, a person with whom he will feel an affinity and whose story will serve as a cautionary tale about being too bent on achieving glory.

You can find this answer in the second letter of the book.  This is a letter that is dated 28th March and is written from Arkangel, a port in Russia.

The letter is written to his sister, Margaret, who is living in England.  In part of this letter, he talks about how sad he is that he wasted his younger days.  He says he wishes that he would have gotten better educated instead of pretty much just teaching himself.

While he is saying that stuff, he tells us that he is 28 years old.