A vizsga után hazamehetsz, ha kész vagy.

A word-for-word breakdown is:

• a = the
• vizsga = exam
• után = after
• hazamehetsz = you can/may go home
• ha = if
• kész vagy = you are ready / you are done

A more literal English order would be:

After the exam, you-can-go-home, if ready you-are.

Hungarian word order does not match English word order exactly, so the natural English translation is smoother than the literal one.

Because után is a postposition, not a preposition.

English uses prepositions:

• after the exam

Hungarian often uses postpositions:

• a vizsga után

So the pattern is:

• noun phrase + postposition

Other common Hungarian postpositions work the same way.

A is the definite article, like English the.

So:

• a vizsga = the exam

Here it most naturally refers to a specific exam already known from context.

You may also see article-less expressions like vizsga után in Hungarian, especially in more general or conversational usage, but a vizsga után is completely normal and clearly means after the exam.

It contains two main parts:

• haza = homeward / to home
• mehetsz = you can/may go

So:

• hazamehetsz = you can go home

Hungarian often combines a directional element like haza with the verb into one written word in a neutral sentence.

It can express either, depending on context.

The form behind mehetsz here often corresponds to English can or may. So hazamehetsz can mean:

• you can go home
• you may go home
• you’re allowed to go home

In this sentence, because it is about what happens after an exam, the most likely meaning is permission:
You may/can go home after the exam if you’re done.

Yes, you can hear both.

• hazamehetsz is a very natural, compact form
• mehetsz haza is also natural, especially in speech

The one-word version often feels like a tighter go home unit. The two-word version is also common and not wrong.

If haza is moved into a specially emphasized position, it can get extra stress or contrast, but in everyday use both attached and separated versions are possible.

Because Hungarian often leaves subject pronouns out when the verb ending already shows the person.

In mehetsz, the ending -sz tells you the subject is you singular.

So Hungarian does not need a separate te here.

Compare:

• mehetek = I can go
• mehetsz = you can go
• mehet = he/she/it can go

The verb ending carries a lot of information.

Because vagy is the 2nd person singular form of lenni = to be.

So:

• kész vagy = you are ready / you are done

In Hungarian present tense, the verb to be is usually:

• used in 1st and 2nd person
• omitted in 3rd person

So:

• én kész vagyok = I am ready
• te kész vagy = you are ready
• ő kész = he/she is ready

That is why vagy must appear here.

It can mean both, depending on context.

In this sentence, because the topic is an exam, ha kész vagy very often means:

• if you’re done
• if you’ve finished

A more general translation if you’re ready is also possible, but in an exam situation English speakers often understand it as if you’re finished with it.

Because Hungarian normally uses a comma before a subordinate clause introduced by ha = if.

So:

• A vizsga után hazamehetsz, ha kész vagy.

This is standard Hungarian punctuation.

That is a difference from English, where a following if-clause often appears without a comma:

• You can go home after the exam if you’re done.

Hungarian is stricter here.

Yes.

You can also say:

• Ha kész vagy, a vizsga után hazamehetsz.

This means essentially the same thing:

• If you’re done, you can go home after the exam.

The difference is mainly about emphasis and information flow. Starting with ha kész vagy puts the condition first.

Because haza expresses movement toward home, while otthon means at home.

So:

• hazamegyek = I go home
• otthon vagyok = I am at home

Since this sentence is about going somewhere, haza is the right choice.