Na farmi djeca prvo žele vidjeti konja i kravu.

Because Croatian normally says na farmi for on/at the farm.

A useful way to think about it is:

• u often means in, inside
• na often means on, at, and it is also used with some places idiomatically

A farm is treated as a place/area where activity happens, so na farmi is the natural expression.

Compare:

• na farmi = on/at the farm
• u kući = in the house

So this is not just literal physical location; it is also about standard Croatian usage.

Because after na when it means location, Croatian uses the locative case.

The base noun is:

• farma = farm

In the locative singular, it becomes:

• na farmi = on/at the farm

So:

• nominative: farma
• locative: farmi

This is a very common pattern with many feminine nouns ending in -a:

• škola → u školi
• ulica → u ulici
• farma → na farmi

Djeca means children, so it is treated as plural.

Even though the form may look unusual to an English speaker, the agreement is plural:

• djeca žele = the children want

Not:

• djeca želi

So the sentence correctly uses the plural verb žele.

This is just an irregular noun you need to learn as a whole:

• dijete = child
• djeca = children

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

So:

• djeca can mean children or the children, depending on context
• konja i kravu can mean a horse and a cow or the horse and the cow, depending on context

Croatian usually leaves definiteness to context, word order, or the situation.

That is why a sentence can be perfectly complete without any article words.

Here prvo means first or first of all.

It is being used as an adverb, modifying the action:

• djeca prvo žele vidjeti... = the children first want to see...

It is not describing a noun, so it does not behave like an adjective such as prvi/prva/prvo meaning first before a noun.

For example:

• prvi konj = the first horse
• prvo žele vidjeti konja = they first want to see a horse

So in your sentence, prvo means first in the sense of before anything else.

Because after željeti (to want), Croatian commonly uses an infinitive for the action wanted.

So:

• žele vidjeti = they want to see
• želim jesti = I want to eat
• želimo ići = we want to go

This is very similar to English want to + verb.

Structure:

• žele = they want
• vidjeti = to see

Together: they want to see

Because vidjeti and gledati are related but not the same.

• vidjeti = to see
• gledati = to look at / watch

In this sentence, the idea is that the children want to see the horse and the cow, probably as the first animals they want to check out on the farm.

If you said žele gledati konja i kravu, it would sound more like they want to watch/look at them for a while.

So vidjeti is the natural choice for simple see.

Because they are direct objects, so Croatian uses the accusative case.

The children want to see what?

• konja = a/the horse
• kravu = a/the cow

So the base forms change like this:

• konj → konja
• krava → kravu

This is completely normal in Croatian.

Because they belong to different noun types.

1. konj is masculine animate

Masculine animate nouns usually have an accusative singular that looks like the genitive:

• nominative: konj
• accusative: konja

Other examples:

• pas → psa
• mačak → mačka

2. krava is feminine

Many feminine nouns ending in -a change to -u in the accusative singular:

• nominative: krava
• accusative: kravu

Other examples:

• žena → ženu
• mačka → mačku

So the different endings come from different gender and declension patterns.

Croatian word order is fairly flexible, so other versions are possible, but they can sound slightly different in emphasis.

Your sentence:

• Na farmi djeca prvo žele vidjeti konja i kravu.

This is natural and puts na farmi first, setting the scene: On the farm...

Other possible orders include:

• Djeca na farmi prvo žele vidjeti konja i kravu.
• Djeca prvo žele vidjeti konja i kravu na farmi.

These are understandable, but the original order is a very natural way to start with the location.

So the order is not random, but it is also not as rigid as in English.