Kamo si stavila mokri kaput da se osuši?

Kamo means where to?, so it is used for direction or destination.

That fits the verb staviti (to put/place), because the question is not just about location in general, but about where the coat was put.

• Kamo si stavila kaput? = Where did you put the coat?
• Gdje je kaput? = Where is the coat?

In everyday speech, some people do use gdje in sentences like this, but kamo is the more precise choice.

This is the Croatian past tense.

Croatian forms the past tense with:

• a present-tense form of biti (to be)
• plus the l-participle

So here:

• si = you are / have (the auxiliary for you singular)
• stavila = the participle of staviti

Together:

• si stavila = you put / you have put

So the structure is literally something like you are put, but in real usage it simply means you put / did you put.

Because the sentence is addressed to a female person.

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

• to a woman: Kamo si stavila...?
• to a man: Kamo si stavio...?
• to more than one person / formal you: Kamo ste stavili...?

So stavila tells you that the speaker is talking to one woman.

Because si is a clitic: a short, unstressed word that usually goes in second position in the clause.

So Croatian often places these little words very early:

• Kamo si stavila...?
• Kad si došla?
• Zašto se smiješ?

This is very normal Croatian word order. English speakers often expect something more like You put where...?, but Croatian organizes these short words differently.

Here kaput is the direct object, so it is in the accusative case.

But kaput is a masculine inanimate noun, and for masculine inanimate nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: mokri kaput
• accusative: mokri kaput

They look identical.

That is why the object does not visibly change here.

Croatian masculine singular adjectives can have a short form and a long form:

• mokar
• mokri

Very roughly, the long form mokri is often used when the noun is more specific/identified, and in everyday usage it is very common before nouns.

So:

• mokri kaput = very natural here
• mokar kaput = also possible in many contexts

A learner does not need to overthink this at first, but it is good to recognize that both forms exist.

This is a purpose clause.

• da = introduces a clause meaning so that, in order that
• se osuši = dries / gets dry

So da se osuši means:

• so that it dries
• so it can dry
• to dry

Croatian often uses da + present tense where English might use:

• to + verb
• or so that + verb

Because the verb here is osušiti se, which means to dry / to become dry.

Compare:

• osušiti nešto = to dry something
• osušiti se = to get dry / to dry

So:

• Osušila sam kaput. = I dried the coat.
• Kaput se osušio. = The coat dried / got dry.

In your sentence, the coat is the thing that becomes dry, so se is needed.

Because after da, Croatian normally uses the present tense form even when the meaning is future or intended.

So:

• da se osuši does not mean only so that it is drying right now
• it means so that it will dry / can dry

This is very common in Croatian. English and Croatian express this idea differently.

Because the subject is understood from context: it is kaput (the coat).

Croatian often leaves subjects unspoken when they are clear.

So in:

• Kamo si stavila mokri kaput da se osuši?

the understood meaning is:

• Where did you put the wet coat so that it could dry?

There is no need to add a separate word for it, because kaput already provides that meaning.

Yes, but the meaning changes a little.

• da se osuši uses a perfective verb and focuses on the result: the coat becomes dry
• da se suši uses an imperfective verb and focuses on the process: the coat is drying

So:

• da se osuši = so that it dries / gets dry
• da se suši = so that it can be drying / so it can dry there for a while

In this sentence, da se osuši is the more natural choice if the goal is that the coat should actually become dry.