Η ακτοπλοϊκή εταιρεία έχει εκδοτήριο εισιτηρίων.

It means ferry company or coastal shipping company.

• εταιρεία = company
• ακτοπλοϊκή is an adjective meaning something like ferry-related / coastal-shipping

So η ακτοπλοϊκή εταιρεία is literally the ferry company.

Because εταιρεία is a feminine singular noun, so it takes the feminine singular definite article η.

The adjective also has to match the noun in gender, number, and case, so:

• η = feminine singular nominative the
• ακτοπλοϊκή = feminine singular nominative
• εταιρεία = feminine singular nominative

Greek adjectives must agree with the nouns they describe.

Because it is the feminine singular nominative form of the adjective.

The adjective is typically listed as:

• ακτοπλοϊκός (masculine)
• ακτοπλοϊκή (feminine)
• ακτοπλοϊκό (neuter)

Since εταιρεία is feminine, Greek uses the feminine form ακτοπλοϊκή.

έχει is the 3rd person singular present tense of έχω (to have).

So:

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

Here the subject is η ακτοπλοϊκή εταιρεία, which is singular, so έχει means has.

Greek often leaves out the indefinite article where English would use a/an.

So:

• έχει εκδοτήριο εισιτηρίων = has a ticket office
• έχει ένα εκδοτήριο εισιτηρίων = also possible, but a little more explicit or emphatic

Without ένα, the sentence sounds very natural and neutral.

εκδοτήριο means ticket office, ticket booth, or issuing office, depending on context.

It comes from the idea of a place where something is issued. In this sentence, it means a place where tickets are sold or issued.

So εκδοτήριο εισιτηρίων is the normal Greek expression for ticket office.

Because it is in the genitive plural.

• singular: το εισιτήριο = the ticket
• plural: τα εισιτήρια = the tickets
• genitive plural: των εισιτηρίων = of the tickets

Greek often uses a structure like:

• noun + genitive noun

So εκδοτήριο εισιτηρίων is literally:

• office/booth of tickets

which English translates more naturally as ticket office.

Because the idea is not an office for one ticket, but a place dealing with tickets in general.

This is very common in Greek. A plural genitive often describes what something handles, sells, or contains.

So:

• εκδοτήριο εισιτηρίων = ticket office
• literally: issuing place of tickets

The plural sounds natural because the office handles many tickets.

It is the direct object of έχει, so it is in the accusative singular.

However, because εκδοτήριο is a neuter noun, its nominative and accusative singular forms are the same.

So the form stays:

• το εκδοτήριο = nominative singular
• το εκδοτήριο = accusative singular as well

That is why you do not see a visible change.

A helpful learner-friendly pronunciation is:

ak-to-plo-i-KEE

The important thing is the ϊ. It shows that the i is pronounced separately, not blended into one sound with the previous vowel.

So you should hear separate parts:

• πλο
• ϊκή

not one merged syllable.

Yes. Greek word order is more flexible than English.

The neutral order here is:

• Η ακτοπλοϊκή εταιρεία έχει εκδοτήριο εισιτηρίων.

But other orders are possible for emphasis, for example:

• Εκδοτήριο εισιτηρίων έχει η ακτοπλοϊκή εταιρεία.

That would sound more marked or emphatic, something like It’s a ticket office that the ferry company has.

For a learner, the original word order is the safest and most natural.

Yes, absolutely.

Both are grammatical:

• Η ακτοπλοϊκή εταιρεία έχει εκδοτήριο εισιτηρίων.
• Η ακτοπλοϊκή εταιρεία έχει ένα εκδοτήριο εισιτηρίων.

The version without ένα is often more natural in straightforward description.
The version with ένα can sound a bit more specific, like has a ticket office / one ticket office.

It follows a very common Greek pattern:

• Subject: Η ακτοπλοϊκή εταιρεία
• Verb: έχει
• Object: εκδοτήριο εισιτηρίων

So the sentence is built just like:

• The ferry company
  • has
    • a ticket office

That makes it a very useful model sentence for learning:

• article + adjective + noun
• present tense of έχω
• noun + genitive noun expression