"They discuss the book about Korea's economy."
Translation:그들은 한국의 경제에 대한 책에 대해 대화해요.
The core sentence is 그들은 대화해요 "they have a conversation/dialogue". 책에 대해 provides the topic: "about (-에 대해) a/the book (책)". Finally, we have a subclause which further describes the book: "about (-에 대한) Korean economy (한국의 경제)".
So far so good, but why are there two different forms for "about"? The answer is that it is in fact the same word (대하다), but when you describe a noun like 책 you need the -한 form, whereas when you use it as an adverb (like here, describing 대화하다), you need the -해(서) form. The reason for this is that the Korean equivalent of "about" is technically not a preposition but an adjective 대하다 (you can think of it as literally meaning "concerning" or "dealing with" if that makes it easier). Therefore you need to use the -ㄴ ending in front of nouns and the -아/어 form (which for verbs/adjectives in -하다 is -해) if you want to use it as an adverb.
Go up to the top of the comments. Look at the second comment by AbunPang. The comment explains the grammar. The grammar rule is -에 대해 means "about" or "concerning." Although we don't say it this way in English, it literally means, "They discuss about the book about Korea's economy."
Naver dictionary says that 대화하다 is "to talk", and as far as I can see from provided example sentences 대화하다 isn't a transitive verb, so it can't take a direct object, and therefore we can't use 를/을 with 책, and in this case, it perfectly matches the way you would say this sentence in English.
talk about the book - 책에 대해 대화해요.
The translation for "discuss the book" would be "책을 이야기해요/ 책을 토론해요", that also well corresponds to the English phrase.