Πριν να φύγουμε, κλείνω την πόρτα του γκαράζ και τις κουρτίνες στο σαλόνι.

Both πριν να φύγουμε and πριν φύγουμε exist in modern Greek and are understood the same way: before we leave.

• πριν φύγουμε: very common, many grammars prefer this form (πριν + subjunctive without να).
• πριν να φύγουμε: also very common in everyday speech and writing; some teachers consider it a bit more colloquial or less “formal”.

In practice, you will hear both all the time.
Grammatically, φύγουμε is in the subjunctive, and πριν (να) introduces a time clause about a future or not-yet-realized event: before we (actually) leave.

The verb φεύγω (to leave) has two main stems:

• φεύγω – present stem (ongoing / repeated / “leaving in progress”)
• φύγω – aorist stem (single, whole event of leaving)

In πριν (να) φύγουμε, we use:

• φύγουμε = 1st person plural, aorist subjunctive

This focuses on the whole event of leaving (the moment we go), not the process.
So the sentence is about one specific departure: Before we (actually) leave…

If you said πριν να φεύγουμε, it would sound odd here; it would suggest “before we are (regularly) in the process of leaving”, which doesn’t fit well.

In Greek, the present tense is often used for:

• Habits / routines: what you usually do
• Fixed sequences: steps you take whenever X happens

Here, κλείνω is:

• κλείνω = 1st person singular, present: I close

So the sentence naturally means:

• Before we leave, I (always / usually) close the garage door and the curtains in the living room.

If you wanted to refer to a specific one-time future action, you could also say:

• Πριν φύγουμε, θα κλείσω την πόρτα… – Before we leave, I will close the door…

Both are correct; the original just emphasizes a general rule or routine.

The subject is “I” (Greek: εγώ).

Greek is a “pro‑drop” language: subject pronouns are often omitted because the verb ending already shows the person and number:

• κλείνω ends in ‑ω → 1st person singular → I close

Adding εγώ is only needed for emphasis or contrast:

• Εγώ κλείνω την πόρτα, εσύ άνοιξε τα φώτα.
  I’ll close the door, you turn on the lights.

η πόρτα is the nominative form (subject of the sentence).
Here, πόρτα is the direct object of κλείνω, so it must be in the accusative:

• η πόρτα (subject: the door closes)
• την πόρτα (object: I close the door)

In this sentence:

• κλείνω την πόρτα → την = feminine accusative singular definite article.

του γκαράζ is a genitive phrase meaning “of the garage” → the garage door.

• το γκαράζ – nominative/accusative (the garage)
• του γκαράζ – genitive (of the garage)

So:

• την πόρτα του γκαράζ = the door of the garage → the garage door.

The noun γκαράζ itself is an indeclinable foreign loan (it doesn’t change form), so the article (το, του) shows the case and role.

Greek usually repeats the definite article with each separate definite noun in a list:

• την πόρτα του γκαράζ και τις κουρτίνες στο σαλόνι
  the garage door and the curtains in the living room

If you said …και κουρτίνες, it would sound more like “and (some) curtains”, making them less specifically identified.

So, with two clear, specific objects, the natural pattern is:

• την πόρτα … και τις κουρτίνες …

στο is a contraction of:

• σε + το → στο

σε is a very common preposition (in, at, on, to), and το is the neuter definite article (the). Together:

• στο σαλόνι = σε + το σαλόνι → in the living room

You will also see other contractions:

• σε + την → στη(ν)
• σε + τους → στους
• σε + τις → στις

Both could be translated as “the curtains in the living room”, but the nuance is slightly different:

• τις κουρτίνες στο σαλόνι – focuses on location right now:
  the curtains (that are) in the living room

• τις κουρτίνες του σαλονιού – focuses on belonging to the living room:
  the living room’s curtains, the curtains of that room in general.

In everyday speech, τις κουρτίνες στο σαλόνι is very natural when describing what you actually go and close.

κουρτίνα is feminine; its plural:

• οι κουρτίνες – nominative plural (subject)
• τις κουρτίνες – accusative plural (object)

In the sentence, κουρτίνες is also a direct object of κλείνω, so we use the accusative article:

• κλείνω τις κουρτίνες → I close the curtains.

γκαράζ is:

• neuter: it takes το, του, στο, etc.
• indeclinable: its form stays γκαράζ in all cases.

Examples:

• το γκαράζ – the garage (subject or object)
• του γκαράζ – of the garage
• στο γκαράζ – in / at the garage

The case is indicated only by the article, not by changing the noun.

You can say Κλείνω το γκαράζ, and it would be understood, but it feels less precise.

• κλείνω το γκαράζ – I close the garage (implies closing whatever needs to be closed: door, shutter, gate)
• κλείνω την πόρτα του γκαράζ – I close the garage door (very specific: the door itself)

In everyday Greek, if there is a physical door, την πόρτα του γκαράζ is more exact.

The part Πριν να φύγουμε is a subordinate time clause (before we leave). Greek punctuation usually separates such introductory clauses with a comma, very much like English:

• Πριν να φύγουμε, κλείνω…
  Before we leave, I close…

If the sentence were reversed, you’d normally omit the comma:

• Κλείνω την πόρτα του γκαράζ και τις κουρτίνες στο σαλόνι πριν να φύγουμε.

You can change word order in Greek, but not all orders sound equally natural.

Your version:

• Κλείνω την πόρτα του γκαράζ και στο σαλόνι τις κουρτίνες

is grammatically possible, but a bit less smooth. It puts στο σαλόνι between και and τις κουρτίνες, which draws attention to the location in a slightly marked way.

The most neutral and natural version is the original:

• Κλείνω την πόρτα του γκαράζ και τις κουρτίνες στο σαλόνι.

This keeps each noun close to its descriptive phrase:

• την πόρτα του γκαράζ
• τις κουρτίνες στο σαλόνι

In contemporary Greek:

• πριν φύγουμε – often considered a bit more “standard” or textbook.
• πριν να φύγουμε – very common in colloquial and everyday speech; many speakers use it instinctively.

Neither is strongly formal or slang; both are widely used. If you want to keep things very simple and close to what many grammars teach, you can prefer:

• Πριν φύγουμε, κλείνω την πόρτα του γκαράζ και τις κουρτίνες στο σαλόνι.