Az azonosításhoz megmutatom a bankszámlakivonatot, és az ügyintéző ellenőrzi az egyenleget.

The ending -hoz means to / for / for the purpose of in this sentence.

• azonosítás = identification
• azonosításhoz = for identification / for the identification process

This is the allative ending, whose basic meaning is movement toward something, but it is also often used in expressions meaning for something.

So:

• Az azonosításhoz = For identification

Because of vowel harmony, this ending can appear as:

• -hoz
• -hez
• -höz

Here it is -hoz.

The first Az is the definite article: the.

The second word, azonosításhoz, just happens to begin with a as part of the noun. So this is not repetition of the same word in the same function.

• Az = the
• azonosításhoz = for identification

So Az azonosításhoz literally breaks down as:

• Az = the
• azonosításhoz = for identification

In natural English, you would usually just say For identification rather than For the identification.

The prefix meg- often gives the verb a completed, definite, result-oriented sense.

• mutat = show
• megmutat = show, show fully, show someone something

In many everyday contexts, Hungarian prefers megmutat when you mean to show someone something as a complete act.

So:

• megmutatom a bankszámlakivonatot = I show / I will show the bank statement

Also, megmutatom is in the definite conjugation, because the object is definite: a bankszámlakivonatot (the bank statement).

The -om ending shows:

• 1st person singular = I
• definite conjugation

So megmutatom means I show it / I am showing the specific thing.

Hungarian uses two main verb conjugations:

1. indefinite conjugation
2. definite conjugation

Here the object is definite:

• a bankszámlakivonatot = the bank statement

Because the object is definite, Hungarian uses the definite form:

• megmutatom

Compare:

• Megmutatok egy kivonatot. = I show a statement.
• Megmutatom a kivonatot. = I show the statement.

The ending -ot marks the direct object. This is the accusative case.

• bankszámlakivonat = bank statement
• bankszámlakivonatot = bank statement + accusative = the bank statement as the thing being shown

Hungarian marks direct objects with -t, but the exact form changes a bit depending on pronunciation, so here it becomes -ot.

So:

• megmutatom a bankszámlakivonatot = I show the bank statement

The direct object is what receives the action of the verb.

Hungarian very often forms compound nouns by writing them as one word.

Here:

• bank = bank
• számla = account / bill
• kivonat = extract / statement

Together:

• bankszámlakivonat = bank account statement, usually just bank statement

This is completely normal in Hungarian. English often uses separate words where Hungarian prefers a single compound word.

Ügyintéző is a person who handles official or administrative matters. Depending on context, it can mean:

• clerk
• administrator
• case handler
• customer service representative
• bank clerk

In this sentence, the most natural translation is something like the clerk or the bank employee handling the matter.

It comes from:

• ügy = matter, case, affair
• intéző = one who manages/handles

So it is literally something like a person who handles the case/matter.

This is again the definite conjugation.

• ellenőriz = to check
• ellenőrzi = he/she checks it

The subject is:

• az ügyintéző = the clerk

And the object is definite:

• az egyenleget = the balance

Because the object is definite, Hungarian uses the definite verb form:

• ellenőrzi

Compare:

• Az ügyintéző ellenőriz egy adatot. = The clerk checks a piece of data.
• Az ügyintéző ellenőrzi az egyenleget. = The clerk checks the balance.

This is also the accusative ending, marking the direct object.

• egyenleg = balance
• egyenleget = balance + accusative = the balance as the thing being checked

The basic object marker is -t, but Hungarian often adds a linking vowel, so here you get -et.

So:

• ellenőrzi az egyenleget = checks the balance

Hungarian has two forms of the definite article:

• a
• az

Which one is used depends on the sound that follows:

• a before a consonant sound
• az before a vowel sound

So:

• a bankszámlakivonatot — because bankszámlakivonatot starts with b
• az ügyintéző — because ügyintéző starts with a vowel sound
• az egyenleget — because egyenleget starts with a vowel sound
• az azonosításhoz — because azonosításhoz starts with a vowel sound

This is similar to English a/an.

Hungarian word order is fairly flexible, but changes in word order often change focus or emphasis, not just style.

The sentence as given is neutral and natural:

• Az azonosításhoz megmutatom a bankszámlakivonatot, és az ügyintéző ellenőrzi az egyenleget.

This presents the actions in a straightforward way.

You could move things around, but then the emphasis changes. For example:

• A bankszámlakivonatot megmutatom az azonosításhoz.
  This puts more focus on the bank statement.

• Az egyenleget az ügyintéző ellenőrzi.
  This emphasizes that it is the clerk who checks the balance.

So yes, Hungarian allows movement, but it is not random; it affects what is highlighted.

Very often, yes, the article can be omitted in expressions like this, especially if you are speaking a bit more generally.

• Az azonosításhoz = for the identification / for identification
• Azonosításhoz = for identification

Both can be natural, but the version with the article may sound a bit more specific or complete in context.

Hungarian often uses articles in places where English might not.

Yes. In Hungarian, the simple present can often express:

• a present action
• a habitual action
• a near-future action, depending on context

So:

• megmutatom can mean I show or I will show
• ellenőrzi can mean he/she checks or he/she will check

In this sentence, the exact time is understood from the situation. If this is describing what happens during a bank procedure, English might translate it as either:

• For identification, I show the bank statement, and the clerk checks the balance.
• For identification, I’ll show the bank statement, and the clerk will check the balance.

Both are possible depending on context.