W słoiku na półce trzymamy płatki, a w drugim słoiku suszone owoce.

They are in the locative case.

Why:

• w
  • location usually takes the locative
• na
  • location also usually takes the locative

So:

• słoik → w słoiku
• półka → na półce
• drugi słoik → w drugim słoiku

This is one of the most common patterns in Polish:

• w domu = in the house
• na stole = on the table

If there were motion toward a place instead of location, Polish would often use a different case.

Because this sentence describes location, not movement.

Compare:

• na półce = on the shelf → where something is
• na półkę = onto the shelf → where something is being put

So:

• Słoik jest na półce. = The jar is on the shelf.
• Kładę słoik na półkę. = I put the jar onto the shelf.

In your sentence, the jar is already there, so na półce is correct.

Because Polish usually drops subject pronouns when they are not needed.

The ending of the verb already tells you the subject:

• trzymam = I keep
• trzymasz = you keep
• trzymamy = we keep

So trzymamy already means we keep.
You could say my trzymamy, but that adds emphasis, something like we are the ones who keep.

Here trzymamy means we keep, we store, or we have in the sense of keeping something somewhere.

The basic verb trzymać often means:

• to hold
• to keep
• to store

In this sentence, it is not literal holding in the hand. It means something more like:

• We keep flakes in the jar on the shelf

It is:

• present tense
• 1st person plural
• from the imperfective verb trzymać

Because Polish often omits repeated words when they are easy to understand from context.

The full version would be:

• W słoiku na półce trzymamy płatki, a w drugim słoiku trzymamy suszone owoce.

But repeating trzymamy is unnecessary, so it is left out.

This kind of ellipsis is very common in both Polish and English:

• I drink tea, and she coffee.
• We keep flakes in one jar, and dried fruit in the other.

In this sentence, a links two parallel pieces of information and gives a slight sense of contrast or comparison.

So:

• i = and
• a = and / while / whereas, depending on context

Here a works well because the sentence compares two containers and their contents:

• in one jar: flakes
• in the other jar: dried fruit

So a sounds very natural.

Very roughly:

• i simply adds
• a sets one thing beside another

They are the direct objects of trzymamy, so they are in the accusative case.

But in Polish, many inanimate plural nouns have the same form in nominative and accusative, so there is no visible change.

That is why:

• płatki looks the same
• owoce looks the same

And the adjective also matches:

• suszone owoce

So they are accusative here, but they happen to look like nominative.

Because the adjective must agree with the noun in case, number, and gender.

Since słoiku is locative singular, the adjective must also be locative singular:

• drugi słoik = nominative
• w drugim słoiku = locative

This agreement is a basic rule in Polish:

• duży dom
• w dużym domu

So drugim is there because słoiku is in the locative.

Because the adjective suszone must agree with owoce.

The noun owoce is plural, so the adjective is also plural:

• suszony owoc = dried fruit, singular
• suszone owoce = dried fruit / dried fruits, plural

In this sentence, the phrase is the object of the verb, but for this kind of plural noun, the accusative looks the same as the nominative, so the form stays suszone owoce.

Płatki is a broad everyday word that can mean:

• flakes
• cereal
• breakfast flakes
• oats or cornflakes, depending on context

On its own, płatki is not always super-specific. In a kitchen sentence like this, many learners will understand it as something like:

• cereal flakes
• breakfast cereal
• oats

Native speakers often rely on context for this word.

Most naturally, it describes the jar:

• the jar on the shelf

So the sentence is understood as:

• In the jar that is on the shelf, we keep flakes...

Grammatically, Polish word order can sometimes leave small ambiguities, but in normal usage this reading is the most natural one.

If you wanted to make it even clearer, you could rephrase:

• W słoiku, który stoi na półce, trzymamy płatki... = In the jar that stands on the shelf, we keep flakes...

Yes. Polish word order is fairly flexible because case endings show grammatical roles.

For example, you could also say:

• Płatki trzymamy w słoiku na półce, a suszone owoce w drugim słoiku.

That version puts more focus on what is being kept.

The original sentence sounds natural because it introduces the location/container first, then the contents:

• W słoiku na półce ...
• a w drugim słoiku ...

So yes, the order can change, but the original version is very normal and smooth.

Literally, it is in the second jar.

But in natural English, depending on context, it may sound better as:

• in the other jar
• in the second jar

Polish drugi can sometimes function where English would naturally say other, especially when two items are being contrasted:

• one jar ... the second/other jar

So both translations can make sense, depending on the style of the English sentence.