Ez a vonat modern.

In Hungarian, when a demonstrative like ez (this) comes before a noun, the definite article is normally repeated:

• ez a vonat = this train
• az a ház = that house

So ez a vonat is the normal, correct pattern.
English does not do this, but Hungarian does.

Ez means this.

In this sentence:

• ez a vonat = this train

A useful contrast is:

• ez a vonat = this train
• az a vonat = that train

So ez shows that the train is near the speaker or mentally close in context.

In the present tense, Hungarian usually leaves out the verb to be in third person sentences like this.

So:

• Ez a vonat modern. = This train is modern.

But Hungarian does not say Ez a vonat van modern.

This is a very important pattern:

• A ház nagy. = The house is big.
• A lány okos. = The girl is smart.
• Ez a vonat modern. = This train is modern.

However, in other persons, van or the appropriate form does appear:

• Én modern vagyok. = I am modern.
• Te modern vagy. = You are modern.

So the missing is is completely normal here.

Modern is a normal Hungarian word, although it is an international/borrowed-looking word and resembles English very closely.

That is common in Hungarian with words like:

• modern
• telefon
• hotel

Even if the word looks familiar, it still behaves according to Hungarian grammar when needed.

No. Hungarian adjectives do not agree with nouns the way they do in some other European languages.

So modern stays modern:

• a modern vonat = the modern train
• a modern ház = the modern house
• a modern autók = the modern cars

The adjective itself does not change here for gender or number.

Vonat means train, and yes, it is a very common everyday word.

Examples:

• A vonat gyors. = The train is fast.
• Ez a vonat késik. = This train is late.

It is a basic vocabulary item worth memorizing early.

Yes, you can change the word order, but it changes the emphasis.

The neutral, ordinary sentence is:

• Ez a vonat modern. = This train is modern.

If you say:

• Modern ez a vonat.

that gives extra emphasis to modern, something like:

• This train is modern
• or It’s this train that is modern
• or This train is modern, actually

Hungarian word order is often influenced by focus and emphasis, not just fixed sentence structure. So the version you were given is the most neutral one.

A simple learner-friendly pronunciation guide is:

• ez ≈ ez
• a ≈ aw (short)
• vonat ≈ voh-naht
• modern ≈ mo-dern

A few helpful points:

• Hungarian stress usually falls on the first syllable of each word.
• So you get: EZ a VO-nat MO-dern
• The a in Hungarian is not the same as English a in cat. It is more like a short aw sound.

Hungarian has two forms of the definite article:

• a
• az

The choice depends on the following sound:

• a before a consonant
• az before a vowel

Since vonat begins with v, a consonant, you say:

• a vonat

Compare:

• az autó = the car
• a vonat = the train

That is why the sentence has ez a vonat, not ez az vonat.

Ez a vonat specifically means this train, not just the train.

Compare:

• a vonat = the train
• ez a vonat = this train
• az a vonat = that train

So ez adds the meaning of this.

Yes, in many contexts that is a natural English translation.

Hungarian:

• Ez a vonat modern.

Depending on context, English could express it as:

• This train is modern.
• This is a modern train.

But grammatically, the Hungarian sentence is structured as this train + modern, not literally this is a modern train.

That would be:

• Ezek a vonatok modernek.

Breakdown:

• ezek = these
• a vonatok = the trains
• modernek = modern in plural predicate form

Notice two things:

1. The demonstrative changes:

   • ez = this
   • ezek = these

2. The adjective gets a plural ending when it is used as the predicate:

   • modern → modernek

So singular:

• Ez a vonat modern.

Plural:

• Ezek a vonatok modernek.

Yes, absolutely. It is a fully natural, complete Hungarian sentence.

Hungarian often expresses ideas very efficiently. Because the present-tense is is omitted in third person, a sentence like this can be very short:

• Ez a vonat modern.

But it is fully grammatical and completely natural in everyday Hungarian.