A képernyőn egy új dokumentum van, mellette pedig egy régi fájl.

Képernyő means screen. The ending -n here is a case ending meaning on.

So:

• képernyő = screen
• képernyőn = on the screen

Hungarian usually uses case endings where English uses prepositions. This ending belongs to the superessive case, whose common forms are -on / -en / -ön / -n.

A few examples:

• asztalon = on the table
• széken = on the chair
• földön = on the ground
• képernyőn = on the screen

So instead of saying a separate word for on, Hungarian often adds the meaning directly to the noun.

Because a/az and egy work like the and a/an in English.

• a képernyőn = on the screen
• egy új dokumentum = a new document
• egy régi fájl = an old file

Here, a képernyőn suggests a specific screen that is already known from the situation or context.

But egy új dokumentum and egy régi fájl introduce items as new information, so the indefinite article egy is used.

Also, egy literally also means one, but in sentences like this it usually just functions as a/an.

In this sentence, van means is / there is.

Hungarian word order is much more flexible than English word order, and it often reflects what is being presented as the topic or focus of the sentence.

Here:

• A képernyőn sets the scene: On the screen
• egy új dokumentum introduces what is there: a new document
• van closes the existential statement: there is

So the structure is roughly:

• A képernyőn egy új dokumentum van = On the screen, there is a new document

This is very natural in Hungarian, especially when the location comes first.

Because Hungarian often leaves out a repeated verb when it is easy to understand from the previous clause.

The full version could be:

• A képernyőn egy új dokumentum van, mellette pedig egy régi fájl van.

But repeating van is not necessary, so it is often omitted:

• A képernyőn egy új dokumentum van, mellette pedig egy régi fájl.

This is similar to English ellipsis in sentences like:

• On the left is a photo, and on the right a painting.

Important point: this omission is not because van is generally impossible here. In fact, in this kind of there is sentence, van is normally used. It is omitted in the second clause because it is already understood.

Mellette means next to it / beside it.

It comes from the postposition mellett, which means next to / beside.

Hungarian can attach personal endings to many postpositions:

• mellettem = next to me
• melletted = next to you
• mellette = next to him / her / it
• mellettünk = next to us

So here:

• mellette = next to it

In this sentence, that it most naturally refers to something mentioned earlier in the sentence.

Also note: Hungarian does not distinguish him / her / it in this form. The same word mellette can mean any of those, depending on context.

Pedig is a very common linking word in Hungarian, but it does not always have one single perfect English equivalent.

In this sentence, it adds a sense of parallel contrast or meanwhile / and also / while.

So:

• mellette pedig egy régi fájl is something like
  • and next to it, an old file
  • while next to it, there is an old file
  • and beside it, there is an old file

In many translations, pedig may simply become and.

It is weaker and more neutral than a strong contradiction word like de (but). Here it helps organize the information: one item is here, and beside it there is another item.

Most naturally, it refers to the new document.

So the most likely reading is:

• There is a new document on the screen, and next to it there is an old file.

Why that reading?

Because mellette usually refers to the most relevant previously mentioned singular thing, and here that is egy új dokumentum.

That said, real context matters. If the situation clearly suggests that something is next to the screen, a listener could interpret it that way. But without extra context, the normal reading is next to the new document.

If someone wanted to say clearly next to the screen, they would usually phrase it more directly, for example:

• A képernyő mellett... = next to the screen...

Yes, that is also grammatical, but the emphasis changes slightly.

Compare:

• A képernyőn egy új dokumentum van
  = On the screen, there is a new document
• Egy új dokumentum van a képernyőn
  = There is a new document on the screen

Both can describe the same situation, but the first version puts the location first, as the frame or topic.

So the original sentence feels a bit like:

• As for the screen, there is a new document on it, and next to it an old file.

This is a very common feature of Hungarian: word order often reflects what the speaker wants to foreground.

Not in this kind of phrase.

In:

• egy új dokumentum
• egy régi fájl

the adjectives új (new) and régi (old) stay unchanged.

Hungarian adjectives used directly before a noun usually do not agree with the noun the way adjectives do in many other European languages.

For example:

• új dokumentum = new document
• új dokumentumok = new documents
• új dokumentumban = in a new document

Notice that the endings go on the noun, not on új.

The same with régi:

• régi fájl = old file
• régi fájlok = old files
• régi fájlban = in an old file

So for an English speaker, this is actually fairly friendly: the adjective usually just stays in one form before the noun.