A nyugtát beteszem a táskába, mert holnap a bankban is kérhetik.

Because nyugtát is the accusative form of nyugta.

• nyugta = receipt
• nyugtát = receipt, as the direct object

In this sentence, the receipt is the thing being put into the bag, so Hungarian marks it with -t.

Also notice the vowel change:

• nyugta → nyugtát

That long á before -t is normal for many nouns ending in -a or -e.

beteszem comes from:

• tesz = to put
• be- = in, into

So beteszem means I put it in or, depending on context, I’ll put it in.

The prefix be- shows direction into something. That matches a táskába = into the bag.

So:

• teszem = I put it
• beteszem = I put it in

Because Hungarian verbs have two main conjugation patterns:

• indefinite conjugation
• definite conjugation

Here the object is a nyugtát = the receipt, which is definite, so the verb uses the definite form.

With tesz:

• teszek = I put (something, indefinite)
• teszem = I put it / I put the specific thing

So:

• Beteszek egy nyugtát. = I put in a receipt.
• Beteszem a nyugtát. = I put in the receipt.

Hungarian often uses the present tense for future meaning when the time is clear from context.

Here the sentence contains holnap = tomorrow, so the future time is already obvious.

That means:

• beteszem can mean I put it in or I’ll put it in
• kérhetik can mean they may ask for it

This is very normal in Hungarian. English often uses will, but Hungarian does not need a separate future form here.

These are two different location endings.

• -ba / -be = into
• -ban / -ben = in

So:

• a táskába = into the bag
• a bankban = in the bank

That makes perfect sense here:

• the receipt goes into the bag
• they may ask for it in the bank

This is a very important Hungarian distinction: movement into vs being inside.

Because of vowel harmony.

Hungarian chooses the ending based on the vowels in the word:

• words with back vowels usually take -ba / -ban
• words with front vowels usually take -be / -ben

Here:

• táska has back vowels, so: táskába
• bank has a back vowel, so: bankban

Compare:

• táskába = into the bag
• székbe = into the chair
• bankban = in the bank
• székben = in the chair

Because a / az is the Hungarian definite article, like the in English.

In this sentence, all three nouns are understood as specific:

• a nyugtát = the receipt
• a táskába = into the bag
• a bankban = in the bank

Hungarian uses:

• a before a consonant
• az before a vowel

So:

• a bankban is correct because bank begins with b
• if the next word began with a vowel, you would use az

kérhetik means they may ask for it or they might request it.

It breaks down like this:

• kér = ask for, request
• -het = may / can / might
• the ending marks 3rd person plural with a definite object

So the whole form means something like:

• they may ask for it

The it is not said separately, because Hungarian often leaves it implicit when it is already clear from context. Here it refers to a nyugtát.

Because Hungarian kérni works differently from English ask for.

In Hungarian:

• kér valamit = ask for something / request something

So the thing requested is a direct object, not a prepositional phrase.

That is why the sentence uses the object idea directly:

• a nyugtát ... kérhetik = they may ask for the receipt

English needs for in many cases, but Hungarian does not.

Hungarian often leaves out subject pronouns when the verb ending already shows the subject.

Here kérhetik tells you the subject is 3rd person plural: they.

In context, this probably means something like:

• the bank staff
• the clerks
• the people at the bank

Hungarian very often uses this kind of unspecified they, just as English does.

is usually means also, too, or sometimes even.

In Hungarian, is normally comes after the word or phrase it belongs to.

So:

• a bankban is = also at the bank / in the bank too

This suggests that the receipt may be needed somewhere else as well, and the bank is another place where it might be requested.

Placement matters:

• holnap is = tomorrow too
• a bankban is = in the bank too

So here, is specifically attaches to a bankban.

No. Hungarian word order is fairly flexible, but different orders change the emphasis.

This sentence is a natural, neutral way to say it:

• A nyugtát beteszem a táskába, mert holnap a bankban is kérhetik.

Roughly speaking:

• A nyugtát sets up the topic
• beteszem a táskába says what happens to it
• holnap gives the time
• a bankban is adds the place with also/too
• kérhetik finishes the clause

You can move parts around, but the focus changes. So learners should usually treat this version as the normal, safe one.