Azon kívül, hogy rugalmas a nyitvatartás, a próbanap díjmentes.

It means besides the fact that..., apart from the fact that..., or in addition to the fact that....

So:

• azon kívül = besides that / apart from that
• hogy = introduces the following clause, like that in English

In this sentence, Azon kívül, hogy rugalmas a nyitvatartás... introduces one positive point before adding another one in the main clause.

Hogy introduces a full clause.

Here, the speaker is not just saying besides the opening hours; they are saying besides the fact that the opening hours are flexible. Because a whole statement follows, Hungarian uses hogy.

Compare:

• Azon kívül, hogy rugalmas a nyitvatartás... = Besides the fact that the opening hours are flexible...
• A rugalmas nyitvatartáson kívül... = Besides the flexible opening hours...

So hogy is needed because what follows is a complete clause, not just a noun phrase.

Hungarian normally uses commas to mark subordinate clauses.

There are two comma points here:

• Azon kívül, hogy: the comma appears before hogy, which introduces the subordinate clause
• ...nyitvatartás, a próbanap...: another comma marks the end of that subordinate clause and the start of the main clause

So the structure is:

• subordinate clause: Azon kívül, hogy rugalmas a nyitvatartás
• main clause: a próbanap díjmentes

This punctuation is very normal in Hungarian.

Because Hungarian usually leaves out the verb van in the present tense, third person singular, when the predicate is a noun or adjective.

So:

• rugalmas a nyitvatartás = the opening hours are flexible
• a próbanap díjmentes = the trial day is free of charge

The verb is/are is understood, but not spoken.

You do need the verb in other situations, for example:

• past tense: A próbanap díjmentes volt. = The trial day was free.
• first person: Én fáradt vagyok. = I am tired.
• plural/past/future contexts as needed

This omission is one of the most important basic patterns in Hungarian.

Both are possible, but the word order changes the information focus slightly.

• A nyitvatartás rugalmas = The opening hours are flexible
  This is more topic-first and can sound a bit more neutral.
• Rugalmas a nyitvatartás = The opening hours are flexible
  This puts more emphasis on rugalmas and presents that as the important new information.

Hungarian word order is often about emphasis and information structure, not just grammar. In this sentence, starting with rugalmas highlights that quality.

Nyitvatartás means opening hours, business hours, or opening times.

Even though English usually uses a plural expression, Hungarian often uses the singular noun nyitvatartás as a collective concept.

So:

• a nyitvatartás = the opening hours

This is completely normal. Hungarian and English simply package the idea differently here.

A is the definite article, meaning the.

In this sentence:

• a nyitvatartás = the opening hours
• a próbanap = the trial day

Hungarian often uses the definite article when the thing is specific or understood from context. Here, we are talking about the opening hours and the trial day of a particular place or service, so the definite article is natural.

Próbanap is a compound noun:

• próba = trial / test
• nap = day

Together, próbanap means trial day, try-out day, or sometimes introductory day, depending on context.

Hungarian forms a lot of nouns by combining words into one compound, and they are often written as a single word. That is very common and very productive in the language.

Díjmentes literally means free from charge/fee.

It is built from:

• díj = fee / charge
• mentes = free from / exempt from

So a próbanap díjmentes means the trial day costs nothing.

This word is slightly formal or business-like. You often see it in ads, websites, official texts, and service descriptions.

Yes. A próbanap ingyenes would also be correct.

The difference is mostly style:

• díjmentes = more formal, more like free of charge
• ingyenes = more everyday, more conversational, often just free

So both work, but díjmentes sounds a bit more polished or promotional in this sentence.