Questions & Answers about אם אתה מוצא את הספרים שלי, תחזיר אותם למדף מעל השולחן.
את marks a definite direct object. The verb מוצא takes a direct object here, and הספרים שלי is definite, so Hebrew uses את before it.
English has no equivalent word, so you usually do not translate את at all.
With possession, Hebrew very often uses the definite article: הספרים שלי = my books.
Without ה, ספרים שלי can sound more like some books of mine or books that are mine, not necessarily the specific books the speaker has in mind. In this sentence, the books are specific, so הספרים שלי fits better.
Because מוצא does not show person by itself. It tells you masculine singular, but it could mean something like finding or he finds depending on context, so the subject אתה is needed.
By contrast, תחזיר already clearly means you will return / you should return in masculine singular, so Hebrew can leave out אתה there. Subject pronouns are often omitted when the verb form already makes them clear.