Při vkladu hotovosti na pobočce napište číslo účtu.

Při here means something like during, when, or in the case of.

So:

• Při vkladu hotovosti = when making a cash deposit / during a cash deposit

In instructions and official language, při is very common for setting the situation in which something should be done.

Because při requires the locative case.

The basic noun is:

• vklad = deposit

Its locative singular form is:

• při vkladu = during a deposit / when making a deposit

So this is not a random ending: it is there because při governs the locative.

Hotovosti is in the genitive.

The phrase vklad hotovosti literally means:

• deposit of cash

This is a very common Czech pattern:

• vklad čeho? = deposit of what?
• hotovosti = of cash

So:

• vklad hotovosti = cash deposit

Na pobočce means at the branch or at the bank branch.

• pobočka = branch, office, branch location
• na pobočce = at the branch

In this sentence, it means a physical branch office, not online banking or an ATM.

This is mostly a matter of Czech usage.

Czech often uses na with certain places and institutions where English would use in or at. A branch office is one of those places:

• na pobočce = at the branch

This is simply the normal idiomatic expression. Learners usually just need to memorize it as a set phrase.

Napište is the imperative form of napsat (to write down).

It can mean:

• write
• please write
• write down

In this kind of instruction, napište is used because it is the polite or plural imperative form.

Compare:

• napiš = write! (to one person, informal)
• napište = write! / please write (to several people, or politely to one person)

On forms, notices, and official instructions, Czech very often uses napište.

Yes. In this sentence it sounds polite, standard, and official.

That fits the context very well, because this looks like an instruction on a banking form or at a bank branch.

So the tone is not rude; it is the normal formal way to tell the customer what to do.

It literally means number of account, which in natural English is account number.

Breakdown:

• číslo = number
• účtu = of the account

Again, Czech uses the genitive here:

• číslo čeho? = number of what?
• účtu = of the account

So:

• číslo účtu = account number

Because číslo is followed by the genitive.

The dictionary form is:

• účet = account

But after číslo you need of the account, so the noun changes:

• číslo účtu = account number

This is a very common pattern in Czech:

• jméno firmy = company name
• adresa hotelu = hotel address
• číslo účtu = account number

The sentence is:

• Při vkladu hotovosti na pobočce napište číslo účtu.

A natural breakdown is:

• Při vkladu hotovosti na pobočce = when making a cash deposit at the branch
• napište číslo účtu = write the account number

So the sentence starts with the situation/context, and then gives the instruction.

That word order is very natural in Czech, especially in formal instructions.

Yes. A word-for-word translation would sound a bit stiff in English.

More natural English versions would be:

• When depositing cash at a branch, write the account number.
• For cash deposits at a branch, write the account number.
• When making a cash deposit at the branch, enter the account number.

The Czech sentence is concise and official, so the English equivalent will often sound like an instruction on a form or notice.

A rough pronunciation guide:

• Při ≈ przhee
• vkladu ≈ fklah-doo
• hotovosti ≈ ho-to-vos-ti
• na pobočce ≈ na po-boch-tseh
• napište ≈ na-pish-teh
• číslo ≈ chees-lo
• účtu ≈ ooch-too

A few helpful sound notes:

• ř in při is a famously difficult Czech sound; English does not really have it.
• č sounds like ch in church.
• š sounds like sh.
• í and ú are long vowels.

If you cannot say ř perfectly yet, that is normal. It is one of the hardest Czech sounds for learners.

Yes, absolutely.

The vocabulary and style are typical of:

• bank forms
• payment instructions
• branch notices
• official customer instructions

The sentence is short, formal, and practical, which is exactly how Czech administrative language often sounds.