Ten kubek jest brudny, weź tamten.

Because kubek is a masculine singular noun in Polish, and the demonstrative has to agree with it.

• ten = this, for masculine singular nouns
• ta = this, for feminine singular nouns
• to = this, for neuter singular nouns

So:

• ten kubek = this mug
• ta filiżanka = this cup
• to naczynie = this vessel/container

Polish words like this and that change form depending on the gender of the noun.

Ten means this, and tamten means that.

So in this sentence:

• Ten kubek = this mug
• weź tamten = take that one

A useful way to think about it:

• ten points to something near the speaker
• tamten points to something farther away, or just a different one from the first

In everyday speech, tamten is often used exactly like English that one.

Because Polish can leave out the noun when it is obvious from context.

Here, tamten really means:

• tamten kubek = that mug

But since kubek was already mentioned, Polish naturally shortens it to just tamten.

English does the same thing:

• This mug is dirty, take that one.

So tamten here works like that one.

Good question. Yes, weź takes a direct object, so tamten is in the accusative here. But for masculine inanimate nouns and matching adjectives/demonstratives, the accusative singular is often the same as the nominative singular.

That is why:

• nominative: ten kubek
• accusative: weź ten kubek

and likewise:

• nominative: tamten
• accusative: weź tamten

So the case does change grammatically, but the form happens to stay the same.

If the noun were feminine, you would see a clearer change:

• ta filiżanka jest brudna, weź tamtą

Here tamtą is the feminine accusative form.

Brudny is the adjective dirty, and it has to agree with kubek.

Since kubek is:

• masculine
• singular
• nominative

the adjective must also be:

• masculine
• singular
• nominative

So:

• brudny kubek = a dirty mug
• kubek jest brudny = the mug is dirty

If the noun changed, the adjective would change too:

• filiżanka jest brudna = the cup is dirty
• okno jest brudne = the window is dirty

Weź is the imperative form, meaning take!

The dictionary form of the verb is wziąć = to take.

This verb is irregular, so the imperative is not something very predictable like simply adding one ending. You just need to learn:

• wziąć = to take
• weź = take! (to one person)
• weźcie = take! (to more than one person)

So in the sentence:

• weź tamten = take that one

Weź is pronounced roughly like vesh, but with a softer final sound.

A few pronunciation notes:

• w in Polish sounds like English v
• e is like e in bet
• ź is a soft sound, similar to a very soft zh / j sound

So weź is approximately veź / vesh-soft, though there is no exact English equivalent.

Also, wziąć and weź are related, even though they look quite different.

In the present tense, Polish normally does use jest in sentences like this.

• Ten kubek jest brudny = This mug is dirty

Unlike Russian, for example, Polish does not normally drop the present-tense to be in standard sentences of this kind.

You may sometimes hear very shortened or informal phrases like:

• Ten kubek brudny

but that is not the normal full sentence. For learners, jest is the correct form to use here.

The comma separates two connected parts:

• Ten kubek jest brudny
• weź tamten

In English, you would also often separate these ideas:

• This mug is dirty, take that one.

So the comma marks a pause between the explanation and the command.

Yes, Polish word order is more flexible than English, although not every version sounds equally natural.

The original:

• Ten kubek jest brudny, weź tamten.

is very natural.

You could also say:

• Weź tamten, ten kubek jest brudny.

This is also understandable and natural, but it puts the command first.

Polish often changes word order for emphasis, rhythm, or context. Still, for a neutral statement, the original version is a very good model.

Not exactly. Kubek usually means a mug or a larger handled cup, often for coffee or tea.

By contrast:

• filiżanka usually means a teacup / cup
• kubek usually means a mug

So Ten kubek jest brudny is best understood as This mug is dirty rather than This cup is dirty, although translations can vary depending on context.