Frater ad apodyterium librum quaesitum redit, quia eum ibi reliquit.

Frater is the nominative singular subject of redit: it tells you who is returning.

Latin also has no definite or indefinite article, so frater can mean brother, a brother, or the brother, depending on context.

Because ad with the accusative expresses motion toward a place.

• redit = returns
• ad apodyterium = to the changing room

If the sentence meant in the changing room as a location, you would expect something like in apodyterio instead.

Apodyterium is a neuter second-declension noun, borrowed from Greek, meaning a changing room or dressing room.

Because it is neuter second declension:

• nominative singular: apodyterium
• accusative singular: apodyterium

So the form stays the same here even though it is accusative after ad.

Here quaesitum is the accusative supine of quaerere.

This is a special Latin construction used after a verb of motion to express purpose:

• redit = he returns
• quaesitum = to look for / to seek

So librum quaesitum redit means he returns to look for the book.

That is a very natural question, because the form looks the same as a participle form.

But here the syntax points to the supine, not to a participle:

• it comes after a verb of motion: redit
• it expresses purpose
• it can take its own object: librum

If it were simply a participle agreeing with librum, the phrase would mean something like the sought book. But in this sentence the sense is clearly he returns in order to look for the book.

Librum is the direct object of the verbal idea in quaesitum.

Even though quaesitum is a supine, it still keeps the object that the verb quaerere would normally take:

• quaerere librum = to look for the book
• librum quaesitum = to look for the book

So librum is not the object of redit. It belongs with quaesitum.

After verbs of motion, Classical Latin often uses the supine in -um to show purpose.

So Latin prefers a pattern like:

• venit rogatum = he came to ask
• redit quaesitum = he returns to look for

An English speaker may expect an infinitive, but the supine is the normal idiom in this kind of sentence.

Eum refers back to librum.

It is:

• masculine, because liber is masculine
• singular, because it refers to one book
• accusative, because it is the direct object of reliquit

A useful rule is:

• pronouns agree with their antecedent in gender and number
• their case depends on their job in their own clause

Because the two actions happen at different times.

• redit is the main action happening now: he returns
• reliquit refers to an earlier completed action: he left it

So the sense is:

• he is returning now
• because earlier he left the book there

That is why the perfect tense in reliquit makes good sense.

Latin usually leaves subject pronouns out unless they are needed for emphasis or contrast.

The verb ending already tells you the subject is third person singular:

• redit = he/she/it returns
• reliquit = he/she/it left

Because frater is already present, Latin does not need to add a separate word for he.

Quia means because and introduces a causal clause.

So the sentence is structured like this:

• main clause: Frater ad apodyterium librum quaesitum redit
• reason clause: quia eum ibi reliquit

The second clause explains why he returns.

Because quia normally introduces a reason presented as a fact, and Latin commonly uses the indicative for that.

Here the speaker is stating a straightforward reason:

• quia eum ibi reliquit = because he left it there

So the indicative reliquit is exactly what you would expect.

Latin word order is much more flexible than English word order, because endings show what each word is doing.

This sentence is organized in a very Latin way:

• Frater — subject first
• ad apodyterium — destination
• librum quaesitum — purpose phrase
• redit — main verb
• quia eum ibi reliquit — reason added afterward

A Latin writer can move words around for emphasis, rhythm, or clarity without changing the basic meaning. English has to rely much more heavily on fixed word order.