Kad završi vrtić, odgojiteljica joj vraća bojanku i tri bojice.

Here kad introduces a time clause. It means when or sometimes once.

So:

• Kad završi vrtić = When she finishes kindergarten / Once she finishes kindergarten

This is very common in Croatian for talking about the time when another action happens.

Završi is the present form of the perfective verb završiti.

In Croatian, after words like kad meaning when, a perfective present often refers to a completed action in the future or in a repeated sequence. So kad završi literally looks like present tense, but the meaning is more like:

• when she finishes
• once she has finished

By contrast:

• završava would sound like an ongoing or habitual action
• će završiti is a future form, but after kad, Croatian usually prefers the present form of a perfective verb

So kad završi is the normal pattern.

Because vrtić is the direct object of završiti, and it is a masculine inanimate noun.

In Croatian, masculine inanimate nouns often have the same form in nominative and accusative singular. So:

• nominative: vrtić
• accusative: vrtić

That is why the form stays the same.

Yes.

Without more context, završiti vrtić usually means to finish kindergarten/preschool as a stage of education.

But depending on context, a learner might wonder whether it means when she is done with kindergarten for the day. Croatian can sometimes allow that kind of interpretation, but if you specifically mean for the day, speakers often use a clearer expression, for example something like:

• kad završi u vrtiću
• kad završi s vrtićem za danas

So the exact nuance depends on context.

Odgojiteljica is a female preschool/kindergarten educator or caregiver.

It is more specific than English teacher in a general sense. In Croatian:

• odgojiteljica = a woman working with children in kindergarten/preschool
• učiteljica = usually a primary-school teacher

So odgojiteljica is the natural word here.

Joj is the short dative form of ona.

Here it means:

• to her

It shows the person who receives the returned items.

So in this sentence:

• odgojiteljica joj vraća bojanku i tri bojice
• the teacher returns her the coloring book and three crayons
• more literally: the teacher returns the coloring book and three crayons to her

Because joj is a clitic: a short, unstressed word that has a special position in Croatian.

Clitics usually come near the beginning of the clause, often after the first stressed word or phrase. So:

• odgojiteljica joj vraća ...

is the normal order.

English speakers often want to put pronouns in freer positions, but Croatian short forms like mi, ti, mu, joj, ga, je, se follow clitic placement rules.

Vraća is the present tense of the imperfective verb vraćati.

Here the present tense can sound:

• habitual: this is what happens whenever the situation occurs
• or descriptive/narrative

So the sentence can feel like:

• When she finishes kindergarten, the teacher gives back her coloring book and three crayons.

If you wanted to make it clearly a single future event, many speakers might also say:

• Kad završi vrtić, odgojiteljica će joj vratiti bojanku i tri bojice.

So vraća is not wrong, but it gives a more habitual or descriptive feel than a simple one-time future.

Because bojanku is in the accusative singular.

The noun bojanka is feminine:

• nominative singular: bojanka
• accusative singular: bojanku

It is in the accusative because it is one of the things being returned.

So:

• vraća bojanku = returns the coloring book

Because after the number tri meaning three, Croatian uses a special numeral construction.

With nouns after dva/dvije, tri, četiri, the noun does not stay in the basic singular form. So:

• bojica = one crayon
• tri bojice = three crayons

For many feminine nouns, the form after tri looks like bojice.

So:

• bojanku i tri bojice = a coloring book and three crayons

This is a very important pattern to learn:

• dvije bojice
• tri bojice
• četiri bojice

not tri bojica in this sentence.