Moja kći kaže da je zebra ljepša od žirafe, ali je moj sin najduže gledao slona.

Because moja has to agree with kći in gender, number, and case.

• kći = feminine singular nominative
• so the possessive adjective must also be feminine singular nominative: moja

Compare:

• moj sin = my son (masculine)
• moja kći = my daughter (feminine)

Yes, it is somewhat irregular and learners often notice that quickly.

• Dictionary form: kći = daughter
• In other cases, forms based on kćer- / kćeri- often appear

For example, you may see forms like:

• kći (nominative)
• kćeri (genitive/dative/locative, depending on context)

So even though the sentence only uses kći, it is useful to know that this noun does not decline as simply as many regular feminine nouns.

Here da means that and introduces a subordinate clause.

So:

• kaže da... = says that...

This is very common in Croatian after verbs of speaking, thinking, knowing, etc.

Examples:

• Mislim da je u pravu. = I think that he/she is right.
• Znam da dolazi. = I know that he/she is coming.

Je is the 3rd person singular present form of biti (to be).

So:

• zebra je ljepša = the zebra is more beautiful

Inside the sentence:

• kaže da je zebra ljepša od žirafe = she says that the zebra is more beautiful than the giraffe

Croatian often uses je in exactly the same place where English uses is.

Ljepša is the comparative form of lijepa / lijep (beautiful).

Base adjective:

• lijep = masculine
• lijepa = feminine
• lijepo = neuter

Comparative:

• ljepši = masculine
• ljepša = feminine
• ljepše = neuter

Since zebra is feminine, the adjective must match it:

• zebra je ljepša = the zebra is more beautiful

After od in comparisons, Croatian normally uses the genitive case.

So:

• nominative: žirafa
• genitive: žirafe

That is why you get:

• ljepša od žirafe = more beautiful than the giraffe

This pattern is very common:

• veći od brata = bigger than the brother
• brži od auta = faster than the car

This is about Croatian clitic word order.

The word je is a clitic (an unstressed short form), and clitics usually go in the second position of their clause.

So after ali (but), it is very natural to place je early:

• ali je moj sin...

A more word-for-word English arrangement like ali moj sin je... is less natural here.

This is one of the biggest differences between English and Croatian word order: Croatian is flexible, but clitics have special placement rules.

Because najduže is an adverb, not an adjective.

Here it describes how long the son watched, not what kind of son or elephant he was.

• dugo = for a long time / long
• duže = longer
• najduže = longest

So:

• gledao je najduže = he watched the longest

If you used an adjective like najduži, it would need to describe a noun:

• najduži film = the longest film

But in your sentence, the word modifies the verb gledao, so the adverb najduže is correct.

Because slon is the direct object of gledao, so it must be in the accusative case.

• nominative: slon = elephant
• accusative: slona

So:

• gledao slona = watched the elephant

This happens because slon is a masculine animate noun. In Croatian, masculine animate nouns usually have:

• nominative singular: slon
• accusative singular: slona

Compare:

• vidim psa = I see the dog
• gledam čovjeka = I watch the man

In the Croatian past tense, the active participle agrees with the subject in gender and number.

The subject here is:

• moj sin = masculine singular

So the past form is:

• gledao

Compare:

• moj sin je gledao = my son watched
• moja kći je gledala = my daughter watched
• dijete je gledalo = the child watched

Because Croatian past tense is usually made with:

• a form of biti (to be)
• the past participle

So:

• je gledao = watched / was watching

That means the sentence contains two different je forms with two different jobs:

• da je zebra ljepša...
  Here je means is
• ali je moj sin najduže gledao...
  Here je helps form the past tense

They look the same, but their function is different.

Because the sentence is about duration: the son watched the elephant for the longest time.

The verb gledati is imperfective, which fits ongoing or extended action well.

• gledati = to watch, to look at
• pogledati = to take a look, to glance, to look once

So:

• najduže gledao sounds natural because it refers to how long the action lasted
• najduže pogledao would sound odd, because pogledati is not normally used for extended duration

Yes, Croatian word order is fairly flexible, but not completely free.

For example, the content could be rearranged for emphasis, but clitics like je still have placement rules. The given version sounds natural and clear:

• Moja kći kaže da je zebra ljepša od žirafe, ali je moj sin najduže gledao slona.

Croatian often moves words around to highlight contrast, topic, or emphasis, but the learner should be especially careful with:

• clitic placement (je, se, ga, etc.)
• case endings, which help show grammatical roles even when word order changes