Prodejce nabízí dlouhou záruku.

Because some Czech masculine animate nouns end in -e. This is normal for certain job titles and person words.

So:

• prodejce = seller, vendor
• it is still masculine animate
• in this sentence it is in the nominative singular, because it is the subject

A native English speaker may expect a masculine noun to look more like muž, but Czech has several noun patterns, and prodejce belongs to one of the patterns where masculine animate nouns can end in -e.

Záruku is in the accusative singular.

The verb nabízet takes a direct object, and the thing being offered is the direct object. Here, the thing being offered is the warranty, so záruka changes to záruku.

Compare:

• záruka = nominative singular, dictionary form
• záruku = accusative singular

So the sentence uses záruku because the seller is offering it.

Because adjectives in Czech must agree with the noun they describe in:

• gender
• number
• case

The noun záruka is:

• feminine
• singular
• accusative in this sentence

So the adjective dlouhý changes to the matching form dlouhou.

That is why you get:

• dlouhá záruka = a long warranty, as a subject or dictionary-style phrase
• dlouhou záruku = a long warranty, as a direct object

Nabízí is the 3rd person singular present tense form of nabízet.

It means:

• offers
• is offering
• in some contexts, does offer

Because the subject is prodejce (seller), nabízí means the seller offers.

Czech present tense can cover both a general meaning and a current action, depending on context.

This is about aspect, which is very important in Czech.

• nabízet = imperfective
• nabídnout = perfective

Very roughly:

• nabízet focuses on the action as ongoing, repeated, habitual, or general
• nabídnout focuses on a single completed offer

In a sentence like this, where you are describing what a seller generally offers, nabízí is the natural choice.

Examples:

• Prodejce nabízí dlouhou záruku. = The seller offers a long warranty.
• Prodejce nabídl dlouhou záruku. = The seller offered a long warranty. / made the offer.

Because Czech does not have articles like English a/an and the.

So prodejce can mean:

• a seller
• the seller

And dlouhou záruku can mean:

• a long warranty
• the long warranty

The exact meaning depends on context.

This is very normal in Czech, and learners have to get used to understanding definiteness from the situation instead of from an article.

It can change.

The neutral, most straightforward order here is:

• Prodejce nabízí dlouhou záruku.

That is a standard subject–verb–object order.

But Czech word order is more flexible because case endings show the grammatical roles. For example, you could also say:

• Dlouhou záruku nabízí prodejce.

This still means the same basic thing, but the emphasis is different. It puts more focus on dlouhou záruku.

So the original sentence is the most neutral version, but not the only possible one.

You know mainly from the cases and the verb form.

• prodejce is in the nominative, so it is the subject
• záruku is in the accusative, so it is the direct object
• nabízí is singular, matching the singular subject prodejce

So even if the word order changes, the endings still tell you that:

• the seller is doing the offering
• the warranty is the thing being offered

This is one of the big differences between Czech and English.

A rough pronunciation guide is:

• PRO-deyt-se NA-bí-zí DLOU-hou ZÁ-ru-ku

A few useful notes:

• Czech stress is usually on the first syllable of each word.
• c is pronounced like ts.
• ou is a diphthong, somewhat like the oa/u sound in go plus a glide.
• á and í are long vowels.

So:

• prodejce sounds roughly like PRO-deyt-tse
• nabízí sounds roughly like na-BEE-zee, but with first-syllable stress in Czech
• záruku sounds roughly like ZAA-roo-koo

In many everyday contexts, záruka is very often best translated as warranty.

For example, when talking about products, stores, or sellers, záruka usually refers to the warranty period or guarantee for the product.

So in this sentence, dlouhou záruku most naturally means something like:

• a long warranty
• a long guarantee period

The exact English word depends on context, but in a sales context, warranty is often the most natural choice.