I like the books does not specify particular books, therefore the answer is "J'aime des livres" I like books FULL STOP! It is impossible to see that I like books means books in general. You have a lot of this type of error/deliberate confusion!!!
The reason you choose "J'aime les livres" instead of "J'aime des livres" is because aimer is a verb of appreciation - to like. When ever you have an object following a verb of appreciation such as aimer, you use les instead of des.