Például holnap kezdődhet a próbaidő.

Például means for example. It introduces this sentence as one possible example of when the probation period could begin.

In this sentence, Például holnap kezdődhet a próbaidő means something like For example, the probation period could start tomorrow.

You can also place például in other positions, but at the beginning it very naturally frames the whole sentence as an example.

Holnap means tomorrow. It is a time adverb, so it does not need a case ending here.

Hungarian often uses simple adverbs of time like:

• ma = today
• holnap = tomorrow
• tegnap = yesterday

So holnap by itself already means on tomorrow / tomorrow, and no extra ending is needed.

Kezdődhet means may start, can start, or could start, depending on context.

It comes from the verb kezdődik, which means to begin / to start.
The ending -hat / -het adds a meaning of possibility, permission, or potentiality.

So:

• kezdődik = it starts / it is starting
• kezdődhet = it may start / it could start / it can start

In this sentence, kezdődhet most naturally means could start or may start.

These are related but not the same.

• kezd = to start something
• kezdődik = to start, to begin (by itself)

So:

• A főnök kezdheti a megbeszélést. = The boss can start the meeting.
  Here someone starts something.

• A megbeszélés kezdődhet. = The meeting can begin.
  Here the meeting itself begins.

In your sentence, a próbaidő is not starting something else; it is itself beginning. That is why kezdődhet is the correct form.

Not exactly. It often corresponds to an English idea like to begin rather than a true passive.

Hungarian does not usually use a passive here. Instead, kezdődik is an intransitive verb meaning begins / starts.

So a próbaidő kezdődik is simply the probation period begins.

It is better to think of kezd and kezdődik as a pair:

• kezd valamit = starts something
• kezdődik = begins

Yes, it does refer to the future, but Hungarian often uses a present-based verb form for future meaning when the time is already clear from context.

Here, holnap already tells you that the action is in the future, so Hungarian does not need a separate future tense form.

That is very normal in Hungarian:

• Holnap indulunk. = We leave tomorrow.
• Jövő héten kezdődik. = It starts next week.

In your sentence, the future meaning comes from holnap, while -het adds could / may.

A is the definite article, meaning the.

So a próbaidő means the probation period. This suggests a specific probation period that both speaker and listener can identify from context.

Hungarian uses definite articles quite often, just like English does. Here it sounds natural because we are talking about a particular probation period, not just any probation period in general.

Próbaidő is a compound noun:

• próba = trial, test
• idő = time, period

Together, próbaidő means probation period or trial period.

In work-related contexts, próbaidő very commonly means the employment probation period.

No, Hungarian word order is quite flexible, and changing it often changes emphasis rather than basic meaning.

Your sentence is:

• Például holnap kezdődhet a próbaidő.

This can sound like for example, it could start tomorrow.

Other possible orders include:

• A próbaidő például holnap kezdődhet.
• Holnap kezdődhet például a próbaidő.

These versions are similar in meaning, but the emphasis shifts. In Hungarian, the position right before the verb often gets strong focus. Here that position is occupied by holnap, so tomorrow gets emphasis.

Not always. -hat / -het can express several related meanings, including:

• ability
• possibility
• permission
• uncertainty / tentative prediction

In this sentence, kezdődhet is probably not about ability in the physical sense. It is more about possibility or what may happen.

So the best English equivalents here are usually:

• could start
• may start
• might start

This is due to vowel harmony, an important feature of Hungarian.

The suffix has two common forms:

• -hat
• -het

Which one appears depends on the vowels in the word stem. Since kezdőd- contains front vowels, the front-vowel form -het is used:

• kezdődhet

This is a normal Hungarian pattern, not something special about this one verb.