This is NOT Princess Mononoke. It looks similar but isn't.
It says right on the picture "THE JOURNEY OF SHUNA" but where in Princess Mononoke is Shuna even mentioned? It isn't.

This is from (gasp) the Journey of Shuna, or Juna no Tabi if you want the JP name.

Unfortunately I dont know anything about the book :/

Well, people see a "red elk" and Shuna no Tabi isn't very well known, so what do you expect?