Sąsiad kazał córce zamknąć furtkę, żeby pies znowu nie uciekł.

Here kazał means told / ordered.

The usual pattern is:

kazać komuś coś zrobić = to tell/order someone to do something

So in this sentence:

• Sąsiad = the neighbor
• kazał = told/ordered
• córce = to his daughter
• zamknąć furtkę = to close the gate

Also, kazał is past tense, masculine singular, because sąsiad is a masculine singular noun.

Because kazać requires the person receiving the order to be in the dative case.

So:

• córka = daughter, nominative
• córce = to the daughter, dative

Compare:

• Matka mówi córce. = The mother speaks to her daughter.
• Ojciec kazał córce wrócić. = The father told his daughter to come back.

So córce is there because the structure is kazać komuś.

Because after kazać, Polish normally uses an infinitive for the action that someone is told to do.

So:

• kazał córce zamknąć furtkę
  = he told his daughter to close the gate

This is very similar to English told someone to do something.

Other examples:

• Kazałem mu poczekać. = I told him to wait.
• Nauczyciel kazał uczniom usiąść. = The teacher told the students to sit down.

Because furtka is the direct object of zamknąć, so it goes into the accusative case.

For this noun:

• furtka = nominative
• furtkę = accusative

So:

• Zamknij furtkę. = Close the gate.
• Widzę furtkę. = I see the gate.

This is a very common pattern with feminine nouns ending in -a: in the singular accusative, they often change to -ę.

Not exactly.

• furtka = a small gate, usually for people walking through a fence
• brama = a large gate, often for cars or a wider entrance

So furtka is the natural word if the dog could slip out through a small gate in a fence.

Here żeby means so that / in order that.

It introduces a purpose clause:

• Sąsiad kazał córce zamknąć furtkę, żeby pies znowu nie uciekł.
• The neighbor told his daughter to close the gate so that the dog would not run away again.

Polish often uses żeby when talking about:

• purpose
• intention
• wishes
• preventing something

For example:

• Zamknij okno, żeby nie było zimno. = Close the window so that it won’t be cold.
• Powiedziałem to, żeby ci pomóc. = I said it in order to help you.

That is a very common learner question.

After żeby, Polish often uses a form that looks like past tense, but it does not mean past here. Instead, it expresses something like:

• so that he wouldn’t
• so that he doesn’t
• so that he won’t

So:

• żeby pies nie uciekł
  = so that the dog would not run away

This is standard Polish grammar.

A few similar examples:

• Zamknij drzwi, żeby nie było zimno. = Close the door so that it won’t be cold.
• Powiedz mu, żeby przyszedł wcześniej. = Tell him to come earlier.

So yes, uciekł looks like past tense, but after żeby it has a different function.

This is about aspect.

Polish has two main aspects:

• imperfective: focuses on the process, repetition, or ongoing action
• perfective: focuses on a completed result or single whole action

Here the verb is from the perfective pair:

• uciekać = to be running away / to run away habitually
• uciec → uciekł = to run away successfully, as one complete event

In this sentence, the idea is:

close the gate so that the dog does not manage to escape again

That is why perfective uciekł fits better.

Similarly, zamknąć is also perfective:

• zamykać = to be closing / to close repeatedly
• zamknąć = to close completely, once

So both verbs fit a single completed action/result:

• close the gate
• prevent one escape

Znowu means again.

So:

• pies nie uciekł = the dog didn’t run away
• pies znowu nie uciekł = the dog didn’t run away again

It suggests that this has happened before, or there is a risk of it happening again.

Its position is fairly natural here, right before nie uciekł, but Polish word order is flexible, so you may also see it in slightly different places depending on emphasis.

Yes, Polish word order is fairly flexible, although some versions sound more natural than others.

The original sentence is very natural:

Sąsiad kazał córce zamknąć furtkę, żeby pies znowu nie uciekł.

You could also say:

Żeby pies znowu nie uciekł, sąsiad kazał córce zamknąć furtkę.

That puts more focus on the purpose: so that the dog wouldn’t run away again.

Even though the order can change, the case endings still show who is doing what:

• sąsiad = subject
• córce = indirect object
• furtkę = direct object

So Polish relies less on word order than English does.

Because Polish normally does not use articles like the or a/an.

So:

• sąsiad can mean the neighbor or a neighbor
• córce can mean to his daughter / to the daughter, depending on context
• furtkę can mean the gate

Possession is also often left implicit when it is obvious from context. In this sentence, córce is naturally understood as his daughter unless the context suggests otherwise.

If needed, Polish can be more explicit:

• swojej córce = to his own daughter
• jego córce = to his daughter

But very often that extra information is unnecessary.