A pénteki találkozó után gyorsan hazamegyek.

A is the definite article, equivalent to English the.

So a pénteki találkozó means the Friday meeting or the meeting on Friday.

Hungarian has two forms of the definite article:

• a before most consonant sounds
• az before vowel sounds

Here pénteki starts with a consonant, so it is a.

Péntek means Friday.
The suffix -i turns it into an adjective meaning Friday-related, on Friday, or simply Friday when it comes before a noun.

So:

• péntek = Friday
• pénteki találkozó = Friday meeting

This is very common in Hungarian. English can put a noun directly before another noun, as in Friday meeting, but Hungarian usually needs the adjective form here.

In this sentence, -i makes péntek into an adjective.

So pénteki describes találkozó:

• pénteki találkozó = a meeting that is on Friday

This -i suffix is often used to form adjectives from places, times, or other nouns, for example:

• budapesti = from Budapest / Budapest-related
• mai = today’s
• nyári = summer / summer-related

Because után is a postposition.

English uses prepositions, which come before the noun:

• after the meeting

Hungarian often uses postpositions, which come after the noun phrase:

• a találkozó után
• literally: the meeting after

So a pénteki találkozó után means after the Friday meeting.

Because után itself already marks the relationship after.

So Hungarian does not need an extra ending on találkozó here. The whole phrase is simply:

• a pénteki találkozó után = after the Friday meeting

This is normal with many postpositions: the noun phrase comes first, and the postposition follows it.

Gyorsan means quickly.

It comes from the adjective gyors, meaning fast or quick, plus an adverb-forming ending:

• gyors = fast, quick
• gyorsan = quickly

Hungarian often forms adverbs this way, with endings like -an or -en.

It is made of two parts:

• haza = homeward, to home
• megyek = I go

Together:

• hazamegyek = I go home / I’m going home

A useful thing to notice is that haza is not a direct object here. It is a directional element meaning movement toward home.

Because in this kind of neutral statement, haza is directly attached to the verb.

So:

• hazamegyek = I go home

But Hungarian can separate them in some situations, especially with negation or certain sentence patterns:

• Nem megyek haza. = I’m not going home.
• Haza fogok menni. = I will go home.

So whether it is written together or separated depends on sentence structure.

It is built into the verb form megyek.

Hungarian verbs usually show the subject, so the separate pronoun én = I is often omitted.

So megyek already means I go, and hazamegyek already means I go home.

You could say Én hazamegyek, but that usually adds emphasis, like I am going home.

Because Hungarian very often uses the present tense for future actions when the time is clear from context.

Here the phrase A pénteki találkozó után already sets the action in a later time frame, so gyorsan hazamegyek can naturally mean:

• I go home quickly
• I’m going home quickly
• I’ll go home quickly

depending on context.

So Hungarian does not always need a separate future form where English would use will.

Not completely. Hungarian word order is fairly flexible, and changes in order often change the focus or emphasis rather than the basic meaning.

This sentence has a very natural structure:

• A pénteki találkozó után = time frame
• gyorsan = manner
• hazamegyek = verb

So it feels like:

• After the Friday meeting, I’ll go home quickly.

Other word orders are possible, but they may sound more marked or emphasize a different part of the sentence.

Because gyorsan is describing how the action happens.

In English, adverbs can move around a lot, and Hungarian also allows some flexibility, but putting gyorsan before the verb is a very normal way to say:

• I go home quickly
• I quickly go home

So in this sentence, gyorsan modifies the action of going home.