English Translation
Young people like his books.
shouldn’t this be их?
Молодые люди любят их книги would mean “Young people like their books”, where “their” refers to people who must have been previously mentioned. For instance:
Чуковский и Маршак были одарёнными писателями. Молодые люди любят их книги.
Chukovsky and Marshak were gifted writers. Young people like their books.
If you meant that young people like their own books (that is, the ones they own), you would use свои:
Чуковский и Маршак были одаренными писателями. Молодые люди любят свои книги.
Here, I think that его refers to a single writer:
Чуковский был одарённым писателем. Молодые люди любят его книги.
Chukovsky was a gifted writer. Young people like his books.