Η κάρτα στάθμευσης κατοίκου γράφει τον αριθμό κυκλοφορίας.

This is very normal in Greek. Greek often uses a main noun + one or more genitive nouns where English might use a compound noun or an adjective.

So:

• κάρτα = card
• στάθμευσης = of parking
• κατοίκου = of a resident

Literally, the phrase is something like the card of parking of a resident, but natural English is the resident parking card or the resident’s parking card/permit.

Greek is often more comfortable than English with this kind of noun chain.

Because it depends on κάρτα and describes what kind of card it is.

• στάθμευση = parking
• στάθμευσης = of parking

The genitive is commonly used in Greek to show a relationship like:

• possession
• type
• purpose
• association

So κάρτα στάθμευσης means parking card literally card of parking.

For the same general reason: it is another noun modifying the phrase.

• κάτοικος = resident
• κατοίκου = of a resident

So στάθμευσης κατοίκου means resident parking or more literally parking of a resident.

Altogether:

• κάρτα στάθμευσης κατοίκου = resident parking card

English usually compresses this into a shorter structure, but Greek often keeps the relationships visible through the genitive.

Because the whole phrase is one noun phrase, with κάρτα as the head noun.

• Η κάρτα = the card

The other nouns, στάθμευσης and κατοίκου, function as modifiers in the genitive, so they do not need their own articles here.

This is similar to how English says the parking card rather than the card of the parking in most cases.

Yes, but in Greek γράφει is also very commonly used to mean:

• it says
• it states
• it shows as written
• it has written on it

So in this sentence, Η κάρτα ... γράφει ... means something like:

• The card says...
• The card shows...
• The card has written on it...

That is a very natural use of γράφω in Greek.

Because αριθμό is the direct object of γράφει.

The verb γράφει is acting on τον αριθμό κυκλοφορίας, so Greek uses the accusative:

• ο αριθμός = the number nominative
• τον αριθμό = the number accusative

This is exactly the kind of case change English speakers need to watch for in Greek: the noun changes form depending on its role in the sentence.

Literally it means number of circulation/traffic, but in normal usage it means:

• registration number
• license plate number

So:

• τον αριθμό κυκλοφορίας = the registration number / license plate number

This is a fixed and very common expression in Greek.

Because it modifies αριθμό in the same way that στάθμευσης modifies κάρτα.

• κυκλοφορία = circulation, traffic
• κυκλοφορίας = of circulation/traffic

So:

• αριθμός κυκλοφορίας = registration number

Again, English often turns this into a compound noun, while Greek often uses noun + genitive.

Yes, Greek word order is more flexible than English, because case endings help show what each word is doing.

The sentence as given is neutral and natural:

• Η κάρτα στάθμευσης κατοίκου γράφει τον αριθμό κυκλοφορίας.

You could move things around for emphasis, for example:

• Τον αριθμό κυκλοφορίας γράφει η κάρτα στάθμευσης κατοίκου.

That would sound more marked, with emphasis on the registration number.

So yes, the order can change, but the original version is the most straightforward one.

Here are the basic forms:

• η κάρτα = card
• η στάθμευση = parking
• ο κάτοικος = resident
• γράφω = write
• ο αριθμός = number
• η κυκλοφορία = circulation, traffic

And here are the forms used in the sentence:

• Η κάρτα = nominative singular
• στάθμευσης = genitive singular
• κατοίκου = genitive singular
• γράφει = 3rd person singular present
• τον αριθμό = accusative singular
• κυκλοφορίας = genitive singular

Not literally in the sense that the card is performing an action like a person. Greek often uses verbs like γράφει with objects such as:

• signs
• labels
• notices
• forms
• cards

So Η κάρτα ... γράφει ... means the card has written on it... or the card states...

This is very similar to English sentences like:

• The sign says...
• The form says...

So the Greek sounds perfectly natural.