In apodyterio vestimenta deponunt, deinde in tepidarium intrant.

Because Latin uses in with different cases depending on the meaning:

• in + ablative = in / inside / at a place, with no movement
• in + accusative = into a place, showing movement toward it

So:

• in apodyterio = in the changing room → location, so ablative
• in tepidarium intrant = they enter into the warm room → motion toward, so accusative

This is one of the most important uses of in to learn.

Apodyterio is ablative singular.

The noun is apodyterium, a second-declension neuter noun. Its basic pattern is:

• nominative singular: apodyterium
• accusative singular: apodyterium
• ablative singular: apodyterio

Because in here means in in the sense of location, it takes the ablative, so we get in apodyterio.

Tepidarium is accusative singular, because after in with motion, Latin uses the accusative.

It looks the same as the dictionary form because tepidarium is a neuter second-declension noun. In that declension:

• nominative singular = tepidarium
• accusative singular = tepidarium

So even though the form has not changed, the case has changed because of the grammar of the sentence.

Vestimenta is accusative plural.

Its job is to be the direct object of deponunt:

• deponunt = they put down / take off / lay aside
• vestimenta = clothes

So vestimenta deponunt means they take off their clothes or literally they put down their clothes.

Also notice that vestimentum is a neuter noun, so in the plural:

• nominative plural: vestimenta
• accusative plural: vestimenta

Again, nominative and accusative are the same because it is neuter.

Because Latin often leaves out subject pronouns when the verb ending already shows who the subject is.

Here:

• deponunt = they put down / they take off
• intrant = they enter

The ending -nt tells you the subject is third person plural: they.

So Latin does not need to add ei or another pronoun unless it wants special emphasis.

Not literally in the most basic sense. Deponunt comes from depono, which basically means put down, lay aside, or set aside.

In this context, with vestimenta, it naturally means:

• they take off their clothes
• or more literally, they lay aside their clothes

Latin often uses a verb with a broader literal meaning, and the context gives the more natural English translation.

Deinde means then, next, or after that.

It is an adverb showing sequence:

• first: In apodyterio vestimenta deponunt
• next: deinde in tepidarium intrant

Latin adverbs often have flexible placement, but here deinde neatly marks the second action.

Latin word order is more flexible than English word order because Latin uses case endings to show how words function in the sentence.

English depends heavily on order:

• They take off clothes
• They enter the warm room

Latin can move words around more freely because endings already show what each word is doing.

In this sentence, the order is quite natural:

• In apodyterio = setting first
• vestimenta = object
• deponunt = verb
• deinde = then
• in tepidarium = destination
• intrant = verb

So the order helps the sentence flow, even though it is not identical to English.

They are both second-declension neuter nouns.

That is useful because they follow the same pattern. For example:

• nominative singular: -um
• accusative singular: -um
• ablative singular: -o
• nominative plural: -a
• accusative plural: -a

So if you know one neuter second-declension noun, it helps you recognize the forms of many others.

These are also words connected with Roman baths:

• apodyterium = changing room
• tepidarium = warm room

Because the Latin present tense can cover both ideas.

So intrant can mean:

• they enter
• they are entering

The exact English translation depends on context and what sounds most natural in English.

In a simple narrative like this, English usually prefers they enter.

Yes: a very important rule is that neuter nominative and accusative are always the same, and in the plural they usually end in -a.

You can see that rule in this sentence:

• vestimenta is neuter plural accusative
• tepidarium is neuter singular accusative, and it looks the same as the nominative form

This rule helps a lot when identifying forms in Latin sentences.