Predložila sam da se družimo.

Because this is the Serbian past tense (often called the perfect), which is usually formed with:

• the past active participle: predložila
• the auxiliary verb sam = I am / have as a tense helper

So predložila sam means I suggested.

This pattern is very common in Serbian:

• rekla sam = I said
• videla sam = I saw
• uradila sam = I did

Because the speaker is female.

In Serbian past tense, the participle agrees with the gender of the subject:

• predložila sam = I suggested (said by a woman)
• predložio sam = I suggested (said by a man)

So this sentence is specifically from a female speaker.

This is normal Serbian word order.

The auxiliary sam is a clitic, which means it usually cannot stand freely and tends to appear in the second position of the clause. In practice, that often gives sentences like:

• Predložila sam...
• Juče sam predložila...
• Ja sam predložila...

So sam after the first word or phrase is very typical.

Here da introduces a subordinate clause, similar to that or to an English structure like to / that we should depending on context.

So:

• Predložila sam da... = I suggested that...

In Serbian, after verbs like suggest, want, ask, recommend, you very often get da + present tense instead of an infinitive-based structure.

Because Serbian commonly uses da + present tense where English might use an infinitive or another construction.

So instead of something like I suggested to hang out, Serbian says:

• Predložila sam da se družimo.

Literally, it is closer to:

• I suggested that we hang out
• or I suggested that we spend time together

This is a very important Serbian pattern.

Se is a reflexive particle used with many Serbian verbs. The verb here is:

• družiti se = to socialize, hang out, spend time together

So se belongs to the verb. You usually learn it as part of the whole expression:

• družiti se
• not just družiti

In many cases, leaving out se would sound wrong or would change the meaning.

Družimo is the 1st person plural present tense form of družiti se:

• ja se družim = I hang out / socialize
• ti se družiš = you hang out
• mi se družimo = we hang out

After da, Serbian uses this present-tense form:

• da se družimo = that we hang out / that we spend time together

So the sentence literally has we built into the verb.

Because the two parts have different subjects/functions:

• Predložila sam = I suggested
• da se družimo = that we hang out

The first part is about what I did. The second part is about what I suggested we do.

So the sentence means that I made the suggestion, but the activity involves us/we.

Not always exactly, but it is often a very good translation.

Družiti se can mean:

• hang out
• spend time together
• socialize
• keep each other company

It often has a friendly, social feeling. Depending on context, English might translate it differently.

For example:

• Volim da se družim s prijateljima. = I like hanging out with friends.
• Deca se druže posle škole. = The kids spend time together after school.

So hang out is often natural, but družiti se can be a bit broader.

Because Serbian often drops subject pronouns when the verb already makes the subject clear.

• Predložila sam already tells you I suggested
• it also tells you the speaker is female

So ja is not necessary.

You could say Ja sam predložila da se družimo, but that would usually add emphasis, such as:

• I’m the one who suggested it

Yes, Serbian word order is flexible, although not completely free.

Possible versions include:

• Predložila sam da se družimo.
• Ja sam predložila da se družimo.
• Juče sam predložila da se družimo.

But the clitic sam still tends to stay in second position.

Some rearrangements may sound more natural than others depending on emphasis and context.

A male speaker would say:

• Predložio sam da se družimo.

The only change is:

• predložila → predložio

Everything else stays the same.

It is generally neutral to informal and very natural in everyday speech.

Družiti se sounds friendly and social, so the sentence fits casual conversation well. It is not rude or slangy, but it usually feels more personal and everyday than something very formal.

In formal contexts, people might choose different wording depending on exactly what they mean.