This is the 7393rd most frequent Russian word.
горецкого
"Горецкого" is the genitive or possessive form related to "Горецкий," which can mean "of Goretsky" (a surname) or "of the highlander" (if derived from "горец," meaning highlander).
Here, "Горецкого" is used as a genitive form of the proper noun "Горецкий", indicating possession or authorship of the book.
Я прочитал книгу Горецкого о природе.
I read the book by Goretsky about nature.
In this usage, "Горецкого" refers to something associated with or named after Goretsky, emphasizing a strong relationship between the proper noun and the noun it modifies.
Мы посетили деревню Горецкого в прошлом году.
We visited Goretsky's village last year.
Here, "Горецкого" is used to describe the estate belonging to or closely related to Goretsky, specifically showcasing personal possession or attribution.