Vidim sliku društvene igre.

Because Serbian usually drops subject pronouns when they are already clear from the verb form.

• Vidim already means I see
• So ja vidim is possible, but ja is usually added only for emphasis, contrast, or clarity

So:

• Vidim sliku društvene igre. = I see a picture of a board game.
• Ja vidim sliku društvene igre. = I see a picture of a board game with extra emphasis on I

Vidim is the 1st person singular present tense form of the verb videti (to see).

So:

• ja vidim = I see
• ti vidiš = you see
• on/ona/ono vidi = he/she/it sees

In this sentence, vidim tells you both the action and the subject.

Because sliku is the accusative singular form of slika.

In Serbian, the direct object of a verb like videti usually goes into the accusative case.

• dictionary form: slika = picture
• accusative singular: sliku

So:

• Vidim sliku = I see a picture
• not Vidim slika

This happens because slika is a feminine noun, and many feminine nouns ending in -a change to -u in the accusative singular.

Because it is in the genitive singular after sliku.

The phrase means picture of a board game, and Serbian often expresses of something by putting that noun in the genitive case.

The base phrase is:

• društvena igra = board game

But after slika:

• slika društvene igre = picture of a board game

Both words change because:

• igra → igre in genitive singular
• društvena → društvene to agree with igre

So the adjective and noun both match in gender, number, and case.

Because Serbian often uses case endings instead of separate words like of.

English says:

• a picture of a board game

Serbian says:

• slika društvene igre

Literally, you can think of it as something like:

• picture board game's

That is not good English, of course, but it helps show what the genitive case is doing.

So in Serbian, of is often expressed by the genitive ending, not by a separate word.

Yes, very often it does.

Literally:

• društvena = social
• igra = game

But as a set phrase, društvena igra commonly means board game in everyday Serbian.

Depending on context, it can sometimes feel broader than English board game, but in many learner contexts that is the most natural translation.

Here it is singular: genitive singular.

That is confusing because igre can also be:

• nominative plural of igra = games
• genitive singular of igra = of a game

In this sentence, it must be genitive singular, because it depends on sliku:

• sliku društvene igre = a picture of a board game

So even though igre can look plural, here it means of a game, not games.

Serbian has no articles like a and the, so the sentence by itself does not mark that distinction.

• Vidim sliku društvene igre. can mean:
  • I see a picture of a board game
  • I see the picture of a board game

Context tells you which one is meant.

If Serbian speakers want to be more specific, they can add other words, but the basic sentence itself does not force a or the.

Yes, Serbian word order is more flexible than English word order.

The neutral order here is:

• Vidim sliku društvene igre.

But other orders are possible, for example:

• Sliku društvene igre vidim.
• Društvene igre sliku vidim. — grammatically possible in special contexts, but less natural as a neutral sentence

The endings show the grammatical roles, so Serbian does not rely on word order as strongly as English does. Still, some orders sound more natural than others depending on focus and emphasis.

They are:

• videti = to see
• slika = picture
• društven / more practically društvena in this phrase = social
• igra = game

In the sentence, they appear as:

• vidim = 1st person singular present
• sliku = accusative singular of slika
• društvene igre = genitive singular of društvena igra

So a learner should recognize that the words in real sentences often look different from the dictionary form because of conjugation and declension.

Because adjectives in Serbian agree with the nouns they describe.

The adjective društvena describes igra, so when igra changes case, the adjective changes too:

• društvena igra = nominative singular
• društvene igre = genitive singular

That agreement is a very important part of Serbian grammar. The adjective and noun move together.

Yes. Slika društvene igre is a complete noun phrase, meaning:

• a picture of a board game
• or the picture of a board game, depending on context

Then in your sentence, that whole phrase becomes the object of vidim:

• Vidim [sliku društvene igre].

So you can think of the sentence as:

• Vidim = I see
• sliku društvene igre = a picture of a board game

That is a useful way to break the sentence into chunks.