Trhovec jde kolem farmářského trhu.

Because the preposition kolem requires the genitive case.

The basic dictionary form is:

• farmářský trh = farmers' market

After kolem, that whole noun phrase changes to genitive:

• farmářský trh → farmářského trhu

Both words change because in Czech, an adjective must agree with its noun in gender, number, and case.

Trh is a masculine inanimate noun. Its genitive singular form is trhu.

So:

• nominative: trh
• genitive: trhu

Since kolem takes the genitive, you get kolem trhu and here more specifically kolem farmářského trhu.

Because farmářský is the nominative singular form, the form you would see in a dictionary.

In the sentence, the noun phrase is not in nominative anymore. It is in the genitive singular because of kolem, so the adjective has to change too:

• farmářský trh = nominative
• farmářského trhu = genitive

This kind of agreement is a basic feature of Czech grammar.

Here kolem means something like:

• past
• by
• sometimes around

With a verb of motion such as jde, the most natural interpretation is goes/walks past or goes by.

So the sentence suggests that the market trader is moving along a path that passes the farmers' market.

Because:

• jít = the infinitive, to go / to walk
• jde = he/she/it goes, 3rd person singular present
• chodí = goes habitually, repeatedly, or in general

So:

• Trhovec jde kolem farmářského trhu. = The trader is going/walking past the farmers' market.
• Trhovec chodí kolem farmářského trhu. = The trader goes/walks past the farmers' market regularly.

A native English speaker often needs to learn that Czech distinguishes one current movement in one direction from habitual or repeated movement.

Czech has no articles, so there is no separate word for a or the.

That means:

• trhovec can mean a market trader or the market trader
• farmářského trhu can mean a farmers' market or the farmers' market

Context tells you which meaning is intended.

Trhovec means a market trader or market seller.

It is understandable, but depending on context, Czech speakers might also use other words, for example:

• prodejce = seller
• prodavač na trhu = seller at the market
• stánkař = stallholder

So trhovec is fine grammatically, but it is not the only natural way to express the idea.

Czech often uses an adjective where English uses a noun phrase or possessive structure.

So:

• farmářský trh literally means something like farmer-type / farmer-related market
• in natural English, that becomes farmers' market

You could say trh farmářů, which literally means market of farmers, but farmářský trh is the normal established expression for the type of market.

Yes. Czech word order is more flexible than English word order.

The sentence as given:

• Trhovec jde kolem farmářského trhu.

is a neutral, straightforward order.

You could also say:

• Kolem farmářského trhu jde trhovec.

That is still grammatical, but it changes the emphasis. It sounds more like you are highlighting the place or path first.

Because Czech marks grammatical roles with case endings, word order can move around more than in English.

A simple learner-friendly approximation is:

• trhovec ≈ TR-ho-vets
• farmářského ≈ far-MAA-rsh-keh-ho

A few useful notes:

• ch is one sound, like the sound in Scottish loch or German Bach
• c is pronounced ts
• á is a long vowel
• ř is a special Czech sound; at first, using a plain r is an acceptable approximation for learners

Also, Czech stress usually falls on the first syllable of the word.