Το γκαράζ οχημάτων και η καμπίνα είναι γεμάτα.

Because Greek often uses the genitive after a noun to show what something is for, contains, or is associated with.

So:

• όχημα = vehicle
• οχημάτων = of vehicles / vehicles'

Here, γκαράζ οχημάτων literally means garage of vehicles, which is a natural Greek way to say vehicle garage or garage for vehicles.

Because οχημάτων is being used in a general, descriptive way.

• γκαράζ οχημάτων = a garage for vehicles / vehicle garage
• γκαράζ των οχημάτων = the garage of the vehicles

So without των, the phrase sounds more general and category-like. With των, it would refer to specific vehicles already known in the context.

In Greek, when two definite nouns are joined by και (and), each noun normally keeps its own article.

So:

• το γκαράζ
• η καμπίνα

This is very natural Greek. It works much like saying the garage and the cabin in English, where both nouns are definite.

γκαράζ is neuter, which is why it takes το.

It is also a borrowed word, and in everyday Modern Greek it is usually treated as indeclinable, meaning the noun itself often stays the same while the article shows the grammatical role:

• το γκαράζ = the garage
• του γκαράζ = of the garage
• τα γκαράζ = the garages

So even if the noun looks unchanged, the article still tells you the gender, number, and case.

Because in Modern Greek, είναι is the present-tense form for both:

• he/she/it is
• they are

So Greek does not change the form here the way English does.

Examples:

• Η καμπίνα είναι γεμάτη. = The cabin is full.
• Το γκαράζ και η καμπίνα είναι γεμάτα. = The garage and the cabin are full.

Because the two singular nouns are joined by και, so together they make a plural subject:

• το γκαράζ
• η καμπίνα
• το γκαράζ και η καμπίνα = the garage and the cabin

So the adjective must be plural: γεμάτα = full for the two things together.

Compare:

• Το γκαράζ είναι γεμάτο. = The garage is full.
• Η καμπίνα είναι γεμάτη. = The cabin is full.
• Το γκαράζ και η καμπίνα είναι γεμάτα. = The garage and the cabin are full.

Because the sentence has mixed genders:

• το γκαράζ = neuter
• η καμπίνα = feminine

When Greek has a predicate adjective referring to nouns of different genders, especially things rather than people, the adjective commonly goes into the neuter plural.

That is why you get:

• γεμάτα and not γεμάτες

This is very common in Greek with mixed inanimate nouns.

Because here γεμάτα is a predicate adjective. It comes after είναι and means are full.

Structure:

• X και Y είναι γεμάτα = X and Y are full

If you put the adjective directly with a noun, it becomes an attributive adjective instead:

• η γεμάτη καμπίνα = the full cabin
• το γεμάτο γκαράζ = the full garage

So in this sentence, the meaning is not the full garage and the cabin, but rather the garage and the cabin are full.

Yes. Greek word order is more flexible than English, as long as the grammar stays clear.

For example, you could also say:

• Η καμπίνα και το γκαράζ οχημάτων είναι γεμάτα.

That would still mean the same thing. The difference is mostly one of emphasis or style, not basic meaning.