Moja baka kaže da je ovaj kaput najstariji u ormaru, ali meni se najviše sviđa.

Because moja must agree with baka in gender, number, and case.

• baka = grandmother, feminine singular nominative
• moja = my, feminine singular nominative

So moja baka means my grandmother. Serbian possessive words like moj / moja / moje change their form to match the noun.

This is the normal Serbian way to say says that ... is ...

• kaže = says
• da = that
• je = is

So:

• baka kaže = grandmother says
• da je ovaj kaput najstariji = that this coat is the oldest

In English, that is sometimes optional, but in Serbian da is very commonly used to introduce this kind of clause.

Ovaj means this, and it agrees with kaput.

• kaput is masculine singular
• so the demonstrative must also be masculine singular: ovaj

Together, ovaj kaput means this coat.

Najstariji is the superlative form of star = old.

The pattern is:

• star = old
• stariji = older
• najstariji = oldest

The ending matches kaput, which is masculine singular. Since the coat is being described, the adjective has to agree with it.

So ovaj kaput je najstariji = this coat is the oldest.

Because u can take different cases depending on meaning:

• u + accusative = movement into something
• u + locative = location inside something

Here the meaning is location: the coat is in the closet, not moving into it.

So:

• u ormar = into the closet
• u ormaru = in the closet

That is why Serbian uses the locative form ormaru here.

Because sviđati se works differently from English to like.

Literally, it is closer to:

• it is pleasing to me

So the structure is:

• meni = to me
• se sviđa = is pleasing / appeals

That is why Serbian says:

• Meni se sviđa kaput
  literally: The coat pleases me

rather than using a structure exactly like English I like the coat.

You can also say volim ovaj kaput, but sviđa mi se is extremely common and often sounds more natural for liking how something seems, looks, or appeals to you.

Meni is the dative form of ja.

• ja = I
• meni / mi = to me

It is used because sviđati se takes the person who likes something in the dative.

So:

• Meni se sviđa = I like it
  literally: It is pleasing to me

This is one of the most important things to remember with sviđati se: the person is not in the nominative.

Both can be correct, but they are used a little differently.

• mi = short, unstressed form
• meni = full, stressed form

In this sentence, meni helps create contrast:

• My grandmother says it is the oldest, but I like it the most.

Using meni makes the I / me idea stand out more. A very natural alternative would be:

• ... ali mi se najviše sviđa.

That version is slightly less emphatic.

Here se is part of the verb expression sviđati se. It does not mean self in a literal English sense.

You should learn this verb as a whole unit:

• sviđati se = to be pleasing, to appeal, to be liked

So se is required here:

• Sviđa mi se. = I like it.
• not Sviđa mi.

Many Serbian verbs are learned together with se, and this is one of them.

Najviše means most.

It is an adverb, not an adjective here, because it modifies the verb phrase se sviđa.

So:

• meni se najviše sviđa = I like it the most

Compare:

• najstariji = the oldest (adjective, describing the coat)
• najviše = the most (adverb, describing how much it is liked)

It is not said explicitly, because Serbian often leaves out words that are clear from context.

The thing being liked is understood to be ovaj kaput from the first part of the sentence.

So Serbian does not need a separate word for it here. If you added a subject pronoun, it would usually sound unnecessary unless you wanted extra emphasis.

No, Serbian word order is fairly flexible, but some positions are more natural than others.

This sentence puts meni early for emphasis and contrast:

• ali meni se najviše sviđa = but I like it the most

Other natural variants are possible, for example:

• ali najviše mi se sviđa
• ali mi se najviše sviđa

The meaning stays basically the same, but the emphasis changes a little. The version with meni sounds more contrastive: Grandma says one thing, but as for me, I like it most.

Ali means but and introduces a contrast.

The contrast is:

• grandmother says the coat is the oldest
• the speaker says they like it the most anyway

So ali is the natural conjunction connecting those two ideas.

It literally says the oldest in the closet, but because kaput has already been mentioned, Serbian does not need to repeat the noun.

So the full idea is understood as:

• this coat is the oldest one in the closet
• or more naturally in English: this coat is the oldest coat in the closet

This kind of omission is very common when the noun is already clear from context.