Η Μαρία πρέπει να έμεινε σπίτι, γιατί δεν απαντάει ούτε στα μηνύματα ούτε στο τηλέφωνο.

In Modern Greek, personal names very often take the definite article.

So:

• Η Μαρία = Maria
• Ο Γιάννης = Yannis / John
• Η Ελένη = Eleni

This is completely normal Greek and does not sound like English the Maria. It is just part of everyday grammar.

The article is especially common when talking about someone in a normal statement. It is often left out in some special cases, such as:

• direct address: Μαρία, έλα εδώ
• some headlines or very formal styles

Here πρέπει να does not express obligation. It expresses a logical conclusion or deduction.

So in this sentence:

• Η Μαρία πρέπει να έμεινε σπίτι
  means something like
• Maria must have stayed home
• Maria must be at home, depending on context

The speaker is guessing based on evidence:

• γιατί δεν απαντάει ούτε στα μηνύματα ούτε στο τηλέφωνο
  because she isn’t answering either messages or the phone

Compare:

• Πρέπει να φύγω τώρα = I have to leave now
  obligation
• Πρέπει να έφυγε ήδη = He must have left already
  deduction

So πρέπει να can mean either have to or must in the sense of I conclude that.... Context tells you which one it is.

Because Greek often uses πρέπει να + past form to make a deduction about a past event.

Here the speaker is thinking:

• She is not answering messages.
• She is not answering the phone.
• Therefore, she probably stayed home / ended up staying home.

English often uses must have + past participle:

• must have stayed home

Greek commonly does this with:

• πρέπει να έμεινε σπίτι

So even though English uses must have stayed, Greek does not need a structure exactly matching English. The Greek pattern here is very natural.

These forms express different aspects or time meanings:

• μένει = he/she stays, he/she lives
• έμεινε = he/she stayed, he/she remained
• έμενε = he/she was staying or used to stay

In this sentence, έμεινε is the best fit because it refers to a single inferred event: she stayed home.

If you used έμενε, it would sound more like an ongoing past situation or habit:

• Η Μαρία έμενε σπίτι = Maria was staying at home / used to stay home

That is not what the speaker is trying to say here.

Because σπίτι can be used without an article or preposition in a very common adverb-like way, meaning home or at home.

So:

• μένω σπίτι = I stay home / I stay at home
• πάω σπίτι = I go home
• είμαι σπίτι = I’m home

You can also hear στο σπίτι in many contexts:

• μένω στο σπίτι

Both are possible, but the version without the article is very common and idiomatic when σπίτι means home in a general sense.

So έμεινε σπίτι is a very natural way to say stayed home.

Γιατί can mean both:

• because
• why

You tell the meaning from context.

Here it means because, since it introduces the reason:

• Η Μαρία πρέπει να έμεινε σπίτι, γιατί δεν απαντάει...
• Maria must have stayed home, because she isn’t answering...

As a question word, it means why:

• Γιατί δεν απαντάει;
• Why isn’t she answering?

The comma also helps show that γιατί is introducing an explanation here.

Ούτε ... ούτε ... means neither ... nor ... or not ... either ... or ... depending on how you translate it naturally.

Here:

• δεν απαντάει ούτε στα μηνύματα ούτε στο τηλέφωνο

means:

• she isn’t answering either the messages or the phone
• more naturally: she’s answering neither the messages nor the phone

A useful thing to notice is that Greek keeps the negative δεν with the verb:

• δεν απαντάει ούτε X ούτε Y

That is a normal Greek pattern.

Because the verb απαντάω / απαντώ usually goes with σε when you say what someone answers.

So:

• απαντάω σε ένα μήνυμα = I answer a message
• απαντάω στο τηλέφωνο = I answer the phone

The forms here are contractions:

• στα = σε + τα
• στο = σε + το

So:

• στα μηνύματα = to the messages
• στο τηλέφωνο = to the phone

In natural English, you usually would not translate the to:

• answer the messages
• answer the phone

But in Greek, the preposition σε is part of the normal structure.

Literally, the Greek structure uses σε, yes. But idiomatically it simply means:

• answer the phone
• pick up the phone

So do not translate it too mechanically word for word.

Similarly:

• απαντάει στα μηνύματα = she answers the messages
• απαντάει στο τηλέφωνο = she answers the phone

This is just how Greek builds the verb απαντάω.

Both are correct.

• απαντάει
• απαντά

They are two common present-tense forms of the same verb in everyday Modern Greek. Απαντάει is very common in speech and informal writing, while απαντά is also standard and slightly shorter.

So:

• δεν απαντάει
• δεν απαντά

both mean he/she isn’t answering.

A learner should recognize both as normal.

The sentence as written is very natural:

• Η Μαρία πρέπει να έμεινε σπίτι, γιατί δεν απαντάει ούτε στα μηνύματα ούτε στο τηλέφωνο.

Greek word order is more flexible than English, but the chosen order sounds neutral and clear:

1. Η Μαρία — topic
2. πρέπει να έμεινε σπίτι — the deduction
3. γιατί... — the reason

You could change the order for emphasis, but this version is the most straightforward one for everyday speech.

For example, moving pieces around might sound more emphatic or marked, but not more basic. So for a learner, this sentence is a good model to copy.