Djeca ne smiju preskočiti ogradu u parku.

Ne smiju is the 3rd person plural of smjeti with negation.

• smjeti = to be allowed to / may
• ne smiju = they are not allowed to / they must not

So this is about permission/prohibition, not physical ability.

Compare:

• Djeca ne smiju preskočiti ogradu. = The children must not / are not allowed to jump over the fence.
• Djeca ne mogu preskočiti ogradu. = The children cannot / are unable to jump over the fence.

Because djeca means children, so the verb agrees with a plural subject.

• djeca = children
• therefore: djeca ne smiju... = children are not allowed...

Even though djeca is an irregular form, it still takes plural agreement:

• Djeca su došla. = The children came.
• Djeca ne smiju... = The children must not...

Yes. Dijete means child, and djeca means children.

This is an irregular plural, so you cannot form it in a simple predictable way from dijete. It is just a form you need to learn as a pair:

• dijete = child
• djeca = children

This is similar to learning English child / children rather than child / childs.

Because after modal verbs like smjeti, Croatian normally uses the infinitive.

Pattern:

• smjeti + infinitive
• moći + infinitive
• htjeti + infinitive

So:

• smiju preskočiti = are allowed to jump over
• ne smiju preskočiti = are not allowed to jump over

Here, preskočiti is the infinitive form: to jump over.

The verb preskočiti means to jump over.

You can break it down roughly like this:

• skočiti = to jump
• preskočiti = to jump over / across

So the prefix pre- adds the idea of going over something.

That is why preskočiti ogradu means jump over the fence.

Preskočiti is a perfective verb. It focuses on a single completed act: successfully getting over the fence.

So:

• preskočiti = jump over once / complete the jump
• preskakati = jump over repeatedly, habitually, or in an ongoing way

In this sentence, the idea is a rule against doing that completed action, so preskočiti is natural.

Because ogradu is the accusative singular form of ograda.

• dictionary form: ograda = fence
• accusative singular: ogradu

Here, ogradu is the direct object of preskočiti:

• jump over what? → ogradu

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

• nominative: ograda
• accusative: ogradu

Because u can take different cases depending on meaning:

• u + locative = location (in/at)
• u + accusative = movement into somewhere (into)

Here the meaning is location, so we use locative:

• u parku = in the park / at the park

Compare:

• Djeca su u parku. = The children are in the park.
• Djeca idu u park. = The children are going into/to the park.

Parku is the locative singular of park.

• nominative: park
• locative: parku

It appears here because the preposition u means location in this sentence:

• u parku = in the park

So the phrase is:

• u
  • locative
• u parku

It can be understood as describing the location of the situation, and in practice that often also means the fence is the one in the park.

So English could naturally interpret it as:

• The children must not jump over the fence in the park or
• In the park, children must not jump over the fence

Croatian often allows this kind of slight ambiguity, and context usually makes it clear.

Because Croatian has no articles.

So Croatian does not have separate words for:

• the
• a / an

That means:

• djeca can mean children or the children
• ogradu can mean a fence or the fence

The exact meaning depends on context.

Yes. Croatian word order is fairly flexible.

The sentence as given is a neutral, natural order:

• Djeca ne smiju preskočiti ogradu u parku.

But other orders are possible if you want to emphasize something:

• U parku djeca ne smiju preskočiti ogradu.
  Emphasizes in the park
• Ogradu u parku djeca ne smiju preskočiti.
  Emphasizes the fence

The meaning stays basically the same, but the focus changes.

In Croatian, negation with most verbs is written as a separate word: ne + verb.

So:

• ne smiju
• ne mogu
• ne žele

That is why you write:

• Djeca ne smiju...

A few common negative forms are written together, such as nemam or nisam, but smjeti is not one of those exceptions.