Χωρίς ρεζέρβα δεν θα έφτανα σπίτι, γιατί το λάστιχο έχανε αέρα πολύ γρήγορα.

Because χωρίς + noun already creates an implied condition.

So Χωρίς ρεζέρβα, δεν θα έφτανα σπίτι means something like Without a spare tire, I wouldn’t get home or If I didn’t have a spare tire, I wouldn’t get home.

Greek does not need αν here, because χωρίς already sets up the hypothetical situation.

A more explicit alternative would be:

Αν δεν είχα ρεζέρβα, δεν θα έφτανα σπίτι.

Here ρεζέρβα means spare tire / spare wheel.

In everyday Greek, especially in driving contexts, ρεζέρβα is a very normal word for the spare. It can also mean reserve more generally in other contexts, but here the meaning is clearly car-related.

Because the sentence is talking about a spare tire in general, not a specific spare tire already identified.

• χωρίς ρεζέρβα = without a spare tire
• χωρίς τη ρεζέρβα = without the spare tire

Also, χωρίς takes the accusative case. In this noun, the accusative singular looks the same as the nominative, so the form stays ρεζέρβα.

δεν θα έφτανα is a conditional form, built with θα + imperfect.

So:

• έφτανα = I was arriving / I used to arrive
• θα έφτανα = I would arrive / I would make it
• δεν θα έφτανα = I wouldn’t arrive / I wouldn’t make it

In this sentence, it expresses a hypothetical result: under those circumstances, getting home would not be possible.

That is the normal word order in Modern Greek.

Negation comes before the whole verb phrase:

• δεν θα πάω = I will not go
• δεν θα μπορούσα = I could not / I wouldn’t be able
• δεν θα έφτανα = I wouldn’t arrive

You do not say θα δεν...

Because σπίτι is often used without a preposition to mean home, especially after verbs of motion.

This works a lot like English:

• πάω σπίτι = I’m going home
• γυρίζω σπίτι = I’m returning home
• φτάνω σπίτι = I arrive home

Using στο σπίτι is also possible in some contexts, but σπίτι by itself is very common and idiomatic when the meaning is simply home.

Because έχανε is the imperfect, which shows an ongoing or repeated action in the past.

Here the idea is that the tire was leaking air continuously or kept losing air.

Compare:

• έχανε αέρα = it was losing air / it kept losing air
• έχασε αέρα = it lost air (more like a single event or a completed fact)

The imperfect fits better because the air loss is presented as a continuing problem.

Literally, it means was losing air.

For a tire, that naturally means:

• it was leaking air
• it was going flat

Greek commonly uses χάνω αέρα with tires, balls, and other inflatable things.

For example:

• Το λάστιχο χάνει αέρα. = The tire is losing air.

Yes. λάστιχο can mean different things depending on context, such as:

• tire
• rubber
• hose
• elastic band

In this sentence, because of ρεζέρβα and αέρα, it clearly means tire.

It is a neuter noun, which is why the article is το.

Yes, γιατί can mean both why and because.

The meaning depends on how it is used:

• Γιατί έφυγες; = Why did you leave?
• Έφυγα γιατί νύσταζα. = I left because I was sleepy.

In your sentence, γιατί introduces the reason, so it means because.

You could also use επειδή here, but γιατί is extremely common and natural.

Because Greek word order is fairly flexible, and this is a natural place for the adverb phrase.

Here πολύ γρήγορα modifies the idea was losing air, and placing it at the end sounds smooth and natural:

το λάστιχο έχανε αέρα πολύ γρήγορα

This is close to saying the tire was losing air very quickly.

Other word orders are possible, but they may sound more marked or place emphasis differently. The version in the sentence is a neutral, everyday choice.

Yes. Greek often moves elements around for emphasis or style.

For example, you could also say:

Δεν θα έφτανα σπίτι χωρίς ρεζέρβα, γιατί το λάστιχο έχανε αέρα πολύ γρήγορα.

Putting Χωρίς ρεζέρβα first gives it extra emphasis, as if setting up the situation right away: Without a spare tire...

So the original order is very natural and slightly more dramatic or informative in tone.