Post balneum puella nudis pedibus per cubiculum currere non debet.

Because post is a preposition that takes the accusative case in Latin when it means after.

So:

• post balneum = after the bath / after bathing

Here balneum is the accusative singular form of balneum, -i.

This is something you often just have to memorize with prepositions: different Latin prepositions govern different cases.

Balneum literally means bath or bathing, and depending on context it can also refer to a bathroom or bath-house.

In this sentence, post balneum most naturally means after the bath or after bathing.
So the phrase is probably about what the girl should not do once she has finished bathing.

Because puella is the subject of the sentence.

• puella = the girl
• nominative singular of puella, -ae

She is the one who should not run, so she appears in the nominative.

Because it depends on debet.

The pattern is:

• debet = she ought / she should / she must
• currere = to run

So currere debet literally means she ought to run, and currere non debet means she ought not to run or she should not run.

This is a very common Latin construction:

• debeo + infinitive = ought to / should / must

Here non debet means should not or ought not to. In some contexts it can also be translated must not, depending on how strong the obligation is.

It does not usually mean does not have to.
For that idea, English distinguishes between:

• should not / ought not = it is wrong or unwise to do it
• does not have to = there is no obligation

Latin non debet normally expresses the first idea, not the second.

Because nudis pedibus is an ablative phrase meaning with bare feet or idiomatically barefoot.

This is the ablative of means/instrument or a closely related use of the ablative.

• nudis = ablative plural of nudus
• pedibus = ablative plural of pes

So literally:

• nudis pedibus = with bare feet

Latin often uses the ablative where English uses with or an adverb like barefoot.

If you said nudos pedes, that would be accusative plural, which would not fit this construction.

Because the phrase refers to the girl’s feet in the normal sense of walking or running on both feet.

Latin, like English, commonly uses the plural for body parts that naturally come in pairs:

• pedes = feet
• manus can mean hands
• oculi = eyes

So nudis pedibus is exactly what you would expect for barefoot.

Because per takes the accusative case.

• per = through, across, sometimes around
• cubiculum is accusative singular

So:

• per cubiculum = through the bedroom / across the room

Again, this is a matter of prepositional usage: per regularly governs the accusative.

Cubiculum usually means bedroom or sleeping room.

So per cubiculum means through the bedroom or across the bedroom.
Depending on the wider context, an English translation might simply say across the room, but the Latin word itself specifically suggests a bedroom.

Latin word order is much more flexible than English word order because the endings show how the words function.

In this sentence:

• puella is clearly the subject because it is nominative
• balneum goes with post
• cubiculum goes with per
• currere depends on debet

So Latin does not need a fixed English-style order to make the grammar clear.

The sentence begins with Post balneum to set the scene: After the bath...
Then it gives the subject: the girl
Then an additional detail: with bare feet
Then the place/motion: through the bedroom
Then the action and obligation: should not run

Yes. That is often the most natural English translation.

Latin says:

• nudis pedibus = literally with bare feet

Natural English often prefers:

• barefoot

So puella nudis pedibus per cubiculum currere non debet can be understood as:

• the girl should not run through the bedroom barefoot

In most ordinary contexts, there is little or no difference in meaning: both mean she should not run.

However, word placement can slightly affect emphasis:

• currere non debet = neutral, common way to say should not run
• non currere debet can place the negation more directly before the infinitive, emphasizing not run

In basic reading, you can take both as expressing the same essential idea.

Because Latin has no articles like English the or a/an.

So a noun like puella can mean:

• a girl
• the girl

The context tells you which is better.

Likewise:

• balneum can be a bath or the bath
• cubiculum can be a bedroom or the bedroom

When translating into English, you add the article that sounds most natural in context.