Procjena štete počinje u devet.

Because štete is in the genitive case.

The noun procjena means assessment/evaluation, and it commonly takes what is being assessed in the genitive:

• procjena štete = assessment of the damage
• procjena rizika = assessment of the risk
• procjena vrijednosti = assessment of the value

So štete is the genitive singular of šteta.

Because procjena is the subject of the sentence, so it is in the nominative case.

The sentence structure is basically:

• Procjena štete = the damage assessment
• počinje = begins/starts
• u devet = at nine

Since procjena štete is the thing that starts, it stays in the nominative.

Because the subject, procjena, is singular.

Croatian verbs agree with the subject in person and number:

• procjena počinje = the assessment starts
• procjene počinju = the assessments start

Even though there are two words at the beginning, the head noun is procjena, and that noun is singular.

Počinje is the 3rd person singular present tense of počinjati / početi.

Here it means begins or starts.

Examples:

• Sastanak počinje u osam. = The meeting starts at eight.
• Film počinje kasno. = The film starts late.

In your sentence, počinje matches the singular subject procjena.

In Croatian, clock time is often expressed with u + accusative.

So:

• u devet = at nine
• u pet = at five
• u deset = at ten

This is a very common pattern for saying when something happens.

You can think of it as the standard way to say at nine o’clock.

Yes. It is often understood as a shortened form of u devet sati.

So these are both possible:

• Procjena štete počinje u devet.
• Procjena štete počinje u devet sati.

The version without sati is very natural in everyday Croatian.

No, not in this sentence.

For clock time, Croatian normally uses u + accusative numeral:

• u devet = correct
• na devet = not correct for this meaning
• u devetu = not how you normally say at nine

So if you want to say that something starts at nine o’clock, u devet is the natural choice.

Yes, Croatian word order is fairly flexible.

The neutral order here is:

• Procjena štete počinje u devet.

But other orders are possible for emphasis, for example:

• U devet počinje procjena štete.

This still means the same thing, but it puts more focus on the time.

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

So Croatian simply says:

• procjena štete

Depending on context, that can mean:

• a damage assessment
• the damage assessment
• damage assessment

The exact meaning is understood from the situation.

A rough English-friendly guide would be:

PRO-tsye-na SHTE-te PO-chi-nye oo DE-vet

A few useful points:

• c is pronounced like ts
• č is like ch in church
• nj sounds like the ny in canyon
• š is like sh

So:

• procjena ≈ PRO-tsye-na
• štete ≈ SHTE-te
• počinje ≈ PO-chi-nye

Šteta is the basic dictionary form, called the nominative singular.

In this sentence, you need the genitive singular after procjena, so it becomes štete.

So:

• šteta = damage (base form)
• štete = of damage / damage’s, depending on context

Here:

• procjena štete = assessment of damage

This is a very common pattern in Croatian noun phrases.