A pénztáros ad egy nagy zacskót, és a kenyeret külön teszi bele.

In Hungarian, singular countable nouns often take an article much like in English.

• a pénztáros = the cashier
• egy pénztáros = a cashier

Here a is the definite article, so the sentence is talking about a specific cashier in the situation, not just any cashier in general.

Also note:

• a is used before most consonants
• az is used before vowels

So:

• a pénztáros
• az eladó

Because zacskót is the direct object of ad (gives), and direct objects in Hungarian usually take the accusative ending -t.

So:

• zacskó = bag
• zacskót = a bag / the bag as the thing being given

And egy means a/an here:

• egy nagy zacskó = a big bag
• egy nagy zacskót = a big bag (as object)

Hungarian often omits the indefinite article in some contexts, but in a sentence like this, egy sounds natural because it introduces a big bag as one item being given.

They both function as direct objects in their parts of the sentence, so they both take the accusative.

• zacskó → zacskót
• kenyér → kenyeret

In the first clause:

• A pénztáros ad egy nagy zacskót
  = The cashier gives a big bag.

In the second clause:

• a kenyeret külön teszi bele
  = puts the bread into it separately.

So zacskót is what is given, and kenyeret is what is put in.

This is because Hungarian noun stems can change when endings are added.

The dictionary form is:

• kenyér = bread

But with the accusative, it becomes:

• kenyeret

This is a normal stem change. Hungarian often inserts a vowel or slightly changes the stem to make pronunciation easier.

Other examples like this:

• egér → egeret
• levél → levelet

So kenyeret is just the correct accusative form of kenyér.

This is a very common and important Hungarian grammar point: definite vs. indefinite conjugation.

The verb tesz means to put. In the present tense, 3rd person singular:

• tesz = he/she puts it, with indefinite conjugation
• teszi = he/she puts it, with definite conjugation

Hungarian uses the definite conjugation when the verb has a definite direct object.

Here the object is:

• a kenyeret = the bread

Because that object is definite, Hungarian uses:

• teszi

Compare:

• Kenyeret tesz bele. = He/she puts bread into it.
  (indefinite object)
• A kenyeret teszi bele. = He/she puts the bread into it.
  (definite object)

Because teszi tells you the action put, but not the direction or location. Bele adds the idea into it.

• teszi = puts
• bele = into it

So:

• teszi bele = puts it into it

This is very typical Hungarian usage. The verb gives the basic action, and a verbal prefix or directional word gives the path or direction.

Related forms:

• be = in / into
• bele = into it
• benne = in it

So:

• bele teszi / teszi bele = puts it into it
• benne van = it is in it

Bele is historically made from:

• be = into
• -le / ele / e type pronominal element referring to it

In modern Hungarian, it is best learned as a single form meaning:

• into it

Examples:

• Beteszi a táskába. = He/she puts it into the bag.
• Beleteszi. = He/she puts it into it.
• A kenyeret bele teszi. = He/she puts the bread into it.

In your sentence, bele refers back to the bag: the cashier puts the bread into the bag.

Külön means separately / apart. Its position reflects Hungarian word order, which often highlights what is important or contrasts with something else.

• a kenyeret külön teszi bele

This suggests that the bread is being put in separately, as opposed to together with other items.

Hungarian word order is flexible, but not random. Putting külön before the verb phrase gives it emphasis.

Possible English sense:

• and puts the bread in separately
• and puts the bread in on its own

Hungarian word order is strongly connected to focus, topic, and emphasis, not just grammar.

In this sentence:

• a kenyeret is a topical or already-known item
• külön gets a noticeable emphasis
• teszi bele completes the action

So the sentence feels natural as:

• and the bread, she puts in separately

Other orders are possible, but they may shift the emphasis:

• A kenyeret külön teszi bele.
  Neutral/natural in this context.
• Külön teszi bele a kenyeret.
  Stronger emphasis on separately.
• Bele teszi a kenyeret külön.
  Less natural in many contexts.

For learners, the key idea is: Hungarian word order is flexible, but each order carries a nuance.

Yes, both are present tense, 3rd person singular:

• ad = gives
• teszi = puts

Hungarian often uses the present tense in descriptions of routine actions or step-by-step actions, just like English can:

• The cashier gives a big bag, and puts the bread in separately.

This can describe:

• a habitual action
• a typical procedure
• what is happening in a scene

So there is nothing unusual about the tense here.

Good vocabulary question. Zacskó usually means a small bag, especially a plastic bag, paper bag, or pouch-like bag used for shopping or packaging.

• zacskó = shopping bag, plastic bag, little bag, sack-like bag
• táska = bag in the broader sense, like a handbag, schoolbag, or larger bag

In a supermarket or bakery context, zacskó is very natural.

So:

• egy nagy zacskó = a big bag, likely the kind used for groceries

Because a kenyeret means the bread, referring to a specific bread already understood in the situation.

Hungarian uses the definite article when the listener can identify the item:

• it is visible
• it was already mentioned
• it is obvious from context

At a checkout, the bread is likely a particular loaf among the items being handled, so a kenyeret is natural.

Compare:

• egy kenyeret = a bread / one bread
  This would introduce it more as a new or nonspecific item.
• a kenyeret = the bread
  This points to a specific loaf already identifiable in context.

Yes, in many contexts rakja could also work.

• teszi = puts, places
• rakja = puts, places, sets, often a bit more physical or colloquial depending on context

So:

• a kenyeret külön teszi bele
• a kenyeret külön rakja bele

Both can be understandable and natural, though teszi is a very standard, general verb for put.

Hungarian often has several verbs that overlap in meaning, and the exact choice can depend on style, region, and context.