W bagażniku nie ma już miejsca na kartony.

Because po w meaning in usually requires the locative case when it refers to location.

• bagażnik = the trunk / boot
• w bagażniku = in the trunk

So the noun changes from its dictionary form bagażnik to the locative form bagażniku.

Compare:

• w domu = in the house
• w pokoju = in the room
• w bagażniku = in the trunk

In Polish, when talking about whether something exists or is available somewhere, the negative form is very often nie ma.

So:

• Jest miejsce. = There is room.
• Nie ma miejsca. = There is no room.

This is a very common pattern in Polish. It does not translate word-for-word into English, but it is the normal way to say that something is absent or unavailable.

Other examples:

• Nie ma czasu. = There is no time.
• Nie ma problemu. = There is no problem.
• Nie ma pieniędzy. = There is no money.

Because after nie ma, Polish normally uses the genitive case.

• basic form: miejsce = place / room / space
• genitive form: miejsca

So:

• Jest miejsce. = There is room.
• Nie ma miejsca. = There is no room.

This is an important pattern:

• jest + nominative
• nie ma + genitive

Compare:

• Jest samochód. = There is a car.
• Nie ma samochodu. = There is no car.

Here już means something like any more or any longer in natural English.

So nie ma już miejsca means:

• there is no room anymore
• there is no more room
• there isn’t any room left

Although już often means already, in negative sentences it often gives this no longer / anymore sense.

Compare:

• Już jest dobrze. = It is good already / now.
• Już nie ma problemu. = There is no problem anymore.

Because Polish often uses miejsce na + accusative to mean room/space for something or a place for something.

So:

• miejsce na kartony = room for boxes
• literally: space for boxes / space intended for boxes

This is a fixed and very common pattern:

• miejsce na walizki = room for suitcases
• miejsce na ubrania = room for clothes
• miejsce na książki = space for books

Because after na in the expression miejsce na ..., you use the accusative case.

The singular is:

• karton = box / carton

The plural is:

• kartony = boxes / cartons

For masculine inanimate plural nouns, the accusative plural is usually the same as the nominative plural, so kartony looks unchanged.

That is why you see:

• na kartony

Compare:

• na stoły = for tables
• na dokumenty = for documents
• na rowery = for bicycles

In this sentence, room or space is the most natural English translation.

Even though miejsce often means place, in contexts like this it refers to available capacity.

So:

• nie ma miejsca = there is no room
• nie ma miejsca w samochodzie = there is no space in the car

Polish uses miejsce more broadly than English place in some situations.

Yes. Polish word order is flexible, although the original sentence is very natural.

For example, you could also say:

• Już nie ma miejsca w bagażniku na kartony.
• Na kartony nie ma już miejsca w bagażniku.

These versions shift the emphasis slightly:

• W bagażniku first emphasizes the location.
• Na kartony first emphasizes what there is no room for.
• Już earlier can emphasize the idea of any more.

But W bagażniku nie ma już miejsca na kartony is a normal, neutral sentence.

Because Polish often does not need an explicit subject in existential sentences like this.

In English, we say:

• There is no room...

But Polish does not use a dummy subject like there. Instead, it simply says:

• Nie ma miejsca...

So the sentence is structurally more like:

• In the trunk, there-is-not room for boxes

This is completely normal in Polish.

Yes. Karton can refer to:

• a cardboard box
• a carton
• sometimes a large box for packing

So kartony may be translated as boxes or cartons depending on context. If the meaning has already been provided to the learner, the grammar stays the same either way.

Because a bagażnik here means the enclosed trunk/boot of a car, so Polish uses w = in.

• w bagażniku = in the trunk

Na bagażniku would suggest on a luggage rack or on top of a carrier, not inside the car’s trunk.

So the choice between w and na depends on whether something is understood as being inside or on a surface / rack.