Chcę przedłużyć wypożyczenie.

A very literal breakdown is:

• Chcę = I want
• przedłużyć = to extend / to renew
• wypożyczenie = the loan / the borrowing / the rental

So the structure is basically:

I want + to extend + the loan

In everyday context, this is often used for things like a library loan, a rented item, or some borrowing period.

Because Polish usually leaves out subject pronouns when the verb already shows who is doing the action.

• chcę already means I want
• so ja is not necessary

You could say Ja chcę przedłużyć wypożyczenie, but that adds emphasis, something like:

• I want to extend it

In a neutral sentence, leaving out ja is more natural.

Chcę is the 1st person singular form of the verb chcieć, meaning to want.

So:

• chcę = I want
• chcesz = you want
• chce = he/she/it wants
• chcemy = we want
• chcecie = you all want
• chcą = they want

A learner may also notice the final ę. That is a Polish nasal vowel, and in normal speech it often sounds a bit like en at the end of a word.

This is mainly about aspect, which is very important in Polish verbs.

• przedłużyć = perfective
• przedłużać = imperfective

Here, przedłużyć is more natural because the speaker wants to complete one specific action: renew or extend something once.

So:

• Chcę przedłużyć wypożyczenie = I want to renew the loan
• Chcę przedłużać wypożyczenie would sound more like I want to be extending it / I want to extend it repeatedly, which is not the usual meaning in this context

In service situations, when you want one concrete result, the perfective infinitive is usually the right choice.

It is in the accusative, because it is the direct object of the verb przedłużyć.

You are extending what? → wypożyczenie

However, for this noun, the nominative and accusative forms look the same:

• nominative: wypożyczenie
• accusative: wypożyczenie

That happens because it is a neuter noun.

So even though the case is accusative here, the form does not change.

Wypożyczenie comes from the verb wypożyczyć, meaning to lend out / to borrow out / to rent out, depending on context.

As a noun, wypożyczenie can mean things like:

• a loan
• a borrowing
• a checkout
• sometimes the loan period

In a library context, this sentence usually means something like:

• I want to renew the loan
• I want to extend my borrowing period

So the exact English translation depends on the situation, but the Polish sentence is perfectly natural.

Because Polish has no articles.

English uses:

• a
• an
• the

Polish does not. So wypożyczenie can mean:

• a loan
• the loan

The context tells you which one is meant. In this sentence, the listener would normally understand that the speaker means a specific loan already known in the situation.

It is grammatical and understandable, but in many real-life situations Polish speakers often soften it.

More polite alternatives include:

• Chciałbym przedłużyć wypożyczenie. = I would like to renew the loan.
  used by a male speaker

• Chciałabym przedłużyć wypożyczenie. = I would like to renew the loan.
  used by a female speaker

• Czy mogę przedłużyć wypożyczenie? = Can I renew the loan?

So Chcę przedłużyć wypożyczenie is correct, but it can sound more direct, like I want to extend the loan.

A rough pronunciation guide:

• Chcę ≈ htsen
• przedłużyć ≈ pshed-WOO-zhich
• wypożyczenie ≈ vih-po-zhih-CHEN-ye

A few important sound notes:

• ch sounds like a harsh h
• cz sounds like ch in chop
• rz and ż usually sound like s in measure
• ł sounds like English w
• ę is a nasal vowel; at the end of a word it is often pronounced close to en

You do not need a perfect English-style spelling to learn this, but these sound correspondences help a lot.

Yes, Polish word order is more flexible than English, because grammatical roles are shown more by endings than by position.

The neutral, most natural order here is:

• Chcę przedłużyć wypożyczenie.

Other orders are possible, but they usually sound marked or emphasize something:

• Wypożyczenie chcę przedłużyć.
  emphasizes the loan

• Przedłużyć chcę wypożyczenie.
  sounds unusual unless used for contrast or emphasis

So for normal everyday use, stick with:

Chcę przedłużyć wypożyczenie.