Translation:Let him go to the bookstore and buy the encyclopedia himself.
Yes, that's what сам means: "by himself, on his own". It doesn't mean "for himself".
Сам is the emphatic definite pronoun. Russians use it to emphasize the subject which is performing an action. Сам changes in gender, number and case. For a declension table, see: https://forum.duolingo.com/comment/29965925
In English, we sometimes emphasize a subject by a similar kind of pronoun, saying something like "He himself went into battle."
It's confusing, because in English, "Buy himself a book" means "Buy a book for himself" while "Buy a book himself" means "Buy a book by himself/on his own". The word-order in English makes all the difference, in this particular idiom.
Except it can't be conveyed by tone in English: "...and buy HIMSELF an encyclopedia" doesn't change anything and sounds wrong, while "...and buy an encyclopedia HIMSELF" only emphasises the original meaning. The two sentences mean different things so only one should be accepted.
"Book store" technically means "A collection of books" - the accumulated books held in storage. That's an archaic and little-used phrase, and most people would think you meant "bookstore" with a typo, which should be Duo's approach also, I think - a typo, not a weird usage.
In the UK this is correct spelling for "encyclopaedia" not "encyclopedia". so please stop saying I have a typo
"let him go to the bookstore himself and buy the encyclopedia" wss not accepted. Probably not "perfectly" grammatically correct, but essentially the same exact sentence with different word order. It is this overly punative garbage that akes duolingo so frustrating for language learners and why I will never recommend it as a sole tool for learning to anyone. Maybe stop caring so much about getting people to buy plus and focus more on actual language learning.
Okay now cue shadyarc with his apologist response...