A router a modem mellett van.

Because a is the Hungarian definite article, meaning the.

So:

• a router = the router
• a modem = the modem

Hungarian uses a before consonant sounds and az before vowel sounds:

• a router
• a modem
• az asztal

Even though router and modem are modern/technical words, they still take the normal Hungarian article.

Because both nouns are definite:

• A router = The router
• a modem mellett = next to the modem

In English, this is completely normal too: The router is next to the modem.

Hungarian simply marks both nouns with the definite article when both are specific.

Mellett means next to or beside.

It is a postposition, which means it comes after the noun, not before it like an English preposition.

Compare:

• English: next to the modem
• Hungarian: a modem mellett

So Hungarian often expresses these location relationships with a noun + postposition structure.

Because Hungarian postpositions usually come after the noun phrase they belong to.

So the normal order is:

• a modem mellett = next to the modem
• az asztal alatt = under the table
• a ház előtt = in front of the house

This is one of the big structural differences from English:

• English uses prepositions: they come before the noun.
• Hungarian often uses postpositions: they come after the noun.

That is a very common and important question.

Hungarian often leaves out van in the third person singular present tense when the predicate is a noun or an adjective:

• A router új. = The router is new.
• A router modem. = The router is a modem.
  (This sentence is odd in meaning, but grammatically it shows the pattern.)

But with location, Hungarian normally does use van:

• A router a modem mellett van. = The router is next to the modem.
• A könyv az asztalon van. = The book is on the table.

So in this sentence, van is required because the sentence tells you where something is.

That is a normal Hungarian word order in a neutral sentence.

The structure here is:

• A router = topic / what we are talking about
• a modem mellett = location
• van = is

So:

• A router a modem mellett van.

Hungarian word order is more flexible than English, but it is not random. It often reflects topic and focus.

This version sounds like a neutral statement: As for the router, it is next to the modem.

Yes, Hungarian word order can change for emphasis.

For example:

• A router a modem mellett van.
  Neutral: The router is next to the modem.

You might also hear different orders in context, but they can sound more marked or emphasize a particular part of the sentence.

For a learner, the given version is the safest and most natural neutral order.

Because mellett is a separate postposition, not a case ending attached directly to the noun.

So Hungarian says:

• a modem mellett
• a ház mellett
• a tanár mellett

The noun stays in its basic form, and the location word comes after it.

This is different from some other Hungarian location expressions that use case endings directly on the noun.

They are commonly used in Hungarian as loanwords for modern technology.

Hungarian often takes international technical words and uses them in Hungarian grammar:

• a router
• a modem
• a laptop
• a monitor

Even if the word originally comes from English, Hungarian still treats it like a normal noun in the sentence.

In Hungarian, foreign technical words are often pronounced in a more Hungarian-like way than in English.

A learner should mainly know that:

• Hungarians may pronounce router differently from English.
• The spelling often stays international, but the pronunciation may be adapted.

You do not need perfect native-like pronunciation right away; the key grammar point here is that router behaves like a regular noun and takes the article a.

You would make the noun plural:

• A routerek a modem mellett vannak. = The routers are next to the modem.

Changes:

• router → routerek = routers
• van → vannak = are

So the location expression stays the same, but the subject and the verb both change to plural.