Do tych dżinsów potrzebuję nowego paska, bo stary jest już za krótki.

Because do here means something like for / to go with in this context, and the preposition do requires the genitive case.

So:

• te dżinsy = these jeans (nominative)
• do tych dżinsów = for these jeans / for these jeans here (genitive after do)

In this sentence, do tych dżinsów means for these jeans, in the sense of to wear with these jeans.

Both words are in the genitive plural because they follow do.

Base form:

• te dżinsy = these jeans

After do:

• tych dżinsów

Breakdown:

• te → tych
• dżinsy → dżinsów

This is a normal case change in Polish. English does not do this much, so it often feels unusual at first.

Because the verb potrzebować usually takes the genitive case.

So:

• nowy pasek = nominative: a new belt
• nowego paska = genitive: of a new belt / a new belt after potrzebuję

Examples:

• Potrzebuję wody. = I need water.
• Potrzebuję samochodu. = I need a car.
• Potrzebuję nowego paska. = I need a new belt.

This is one of the key things to remember with potrzebować.

The dictionary form is potrzebować, which means to need.

Potrzebuję is the 1st person singular present tense:

• ja potrzebuję = I need

A quick conjugation:

• (ja) potrzebuję = I need
• (ty) potrzebujesz = you need
• (on/ona/ono) potrzebuje = he/she/it needs
• (my) potrzebujemy = we need
• (wy) potrzebujecie = you all need
• (oni/one) potrzebują = they need

Polish often leaves out a noun when it is obvious from context.

So:

• stary jest już za krótki

really means:

• stary pasek jest już za krótki = the old belt is already too short

Using just stary is natural because the listener already knows we are talking about a belt. English can do this too sometimes, as in I need a new one because the old one is too short.

Here za means too.

So:

• krótki = short
• za krótki = too short

Very common pattern:

• za duży = too big
• za mały = too small
• za drogi = too expensive
• za późno = too late

So stary jest już za krótki means the old one is already too short.

Because the hidden noun is pasek, and pasek is masculine singular.

So the adjective must match it:

• nowy pasek
• stary pasek
• krótki pasek

Even when pasek is omitted, the adjective still agrees with that implied noun:

• stary jest już za krótki

Już usually means already.

So:

• stary jest za krótki = the old one is too short
• stary jest już za krótki = the old one is already too short

It suggests that the belt did fit before, or that the situation has changed over time.

Yes. Polish word order is flexible, and the beginning of the sentence often shows what the speaker wants to emphasize.

This version:

• Do tych dżinsów potrzebuję nowego paska...

puts focus on these jeans: For these jeans, I need a new belt...

You could also say:

• Potrzebuję nowego paska do tych dżinsów...

That is also natural and may sound a bit more neutral to some learners.

Both are correct. The original sentence emphasizes the jeans first.

Yes, bo means because, and it is very common in everyday speech.

So:

• bo stary jest już za krótki = because the old one is already too short

You could also say:

• ponieważ stary jest już za krótki

But ponieważ is usually a bit more formal or careful in tone. In ordinary conversation, bo is extremely common.

Yes, dżinsy is normally used as a plural noun, like English jeans.

So you say:

• te dżinsy = these jeans
• mam nowe dżinsy = I have new jeans
• do tych dżinsów = for these jeans

This kind of noun is often called plural-only or pluralia tantum. Polish has several clothing words like this.

In this sentence, the best natural English idea is for these jeans or to go with these jeans.

Polish do has many uses, and in clothing contexts it often means something like:

• suitable for
• intended for
• matching with

So the speaker is saying they need a new belt for wearing with these jeans.

Yes, but the meaning changes slightly.

• Potrzebuję nowego paska = I need a new belt
• Muszę mieć nowy pasek = I must have a new belt / I have to have a new belt

Potrzebuję is more neutral and natural here.
Muszę mieć sounds stronger, more like a necessity or obligation.

So for this sentence, potrzebuję nowego paska is the more natural choice.

A simple approximation:

• dżinsów ≈ JEEN-soof
• paska ≈ PAHS-kah

A few notes:

• dż sounds like the j in jam
• ó is pronounced like u
• w in Polish is pronounced like English v, but at the end of a word it is often devoiced, so -ów sounds roughly like -oof
• a is usually a clear ah sound

Not very naturally. A word-for-word translation would look something like:

• For these jeans I need a new belt, because the old one is already too short.

That is understandable, but the most natural English version might be:

• I need a new belt for these jeans, because the old one is already too short.

This is a good example of how Polish and English often express the same idea with slightly different structure.