baechureul ssiseun da-eume naembie neohgo gugeul kkeulhyeosseoyo.

씻은 다음에 means after washing or after having washed.

It is made of:

• 씻은 = washed (the verb 씻다, to wash, turned into a modifier)
• 다음에 = after / next

So 배추를 씻은 다음에 literally means after washing the cabbage.

This pattern is very common for showing that one action happens first, and then another action happens after it.

Because when a verb comes before a noun like 다음, it usually changes into a modifying form.

Here:

• 씻다 = to wash
• 씻은 = washed / having washed

Since 다음 is a noun meaning something like next or following, Korean uses the modifier form:

• 씻은 다음에 = after washing

This is similar to how Korean often puts a verb in a descriptive/modifying form before a noun.

Because 배추 is the direct object of 씻다.

• 배추를 씻다 = to wash the cabbage

Here, -를 marks what is being acted on. The cabbage is the thing being washed, so -를 is the natural choice.

If you used 배추가, it would mark 배추 as the subject, which does not fit this sentence well.

Because 냄비 is the place/container something is put into, not the thing being put.

• 냄비에 = into the pot / in the pot
• 넣다 = to put in

So:

• 냄비에 넣고 = put it into the pot, and...

If you said 냄비를 넣고, that would mean the pot itself is the object being put somewhere, which is not the intended meaning.

넣고 comes from 넣다 (to put in) plus -고, which links actions.

So 넣고 means:

• put it in and...
• after putting it in...
• put it in, then...

In this sentence, it connects the action of putting the cabbage into the pot with the next action of cooking/boiling the soup.

-고 connects verbs, similar to and, and then, or sometimes just a simple link between actions.

Here:

• 냄비에 넣고 국을 끓였어요
• put it in the pot and cooked/boiled the soup

In many cases, -고 simply shows that one action is followed by another.

A useful point: Korean often uses -고 even when English would naturally say then.

This is very common in Korean.

When several actions are linked together, usually only the final verb carries the full tense and speech-level ending. The earlier verbs appear in connecting forms.

So:

• 씻은 다음에 = after washing
• 넣고 = put in and
• 끓였어요 = boiled/cooked

Even though only the last verb is fully marked as past polite, the whole sequence is understood as having happened in the past.

Yes, this is natural in Korean.

• 국 = soup
• 끓이다 = to boil / cook / make by boiling

So 국을 끓였어요 means made soup, cooked soup, or literally boiled soup.

In English, make soup or cook soup often sounds more natural than boil soup, but in Korean 국을 끓이다 is a very normal expression.

Because 끓이다 is the transitive verb, meaning to boil something / to cook something by boiling.

• 국을 끓이다 = to cook/boil soup
• 물이 끓다 = water boils

So:

• 국을 끓였어요 = (someone) cooked the soup
• 국이 끓었어요 would mean the soup boiled or the soup has come to a boil

The sentence is talking about a person doing the cooking, so 끓이다 is the correct choice.

The subject is omitted, which is very common in Korean.

The sentence does not explicitly say:

• I washed the cabbage...
• She washed the cabbage...
• They washed the cabbage...

Korean often leaves out the subject when it is clear from context. So depending on the situation, this could mean:

• I washed the cabbage, put it in a pot, and made soup
• She/He washed the cabbage, put it in a pot, and made soup

You usually figure out the subject from the conversation or context.

끓였어요 uses the -어요 / -아요 polite style, often called the informal polite style.

This is one of the most common everyday polite endings in Korean.

So the sentence is polite, but not especially formal. It is appropriate in many normal conversations.

For comparison:

• 끓였어요 = polite everyday speech
• 끓였습니다 = more formal
• 끓였어 = casual, used with close friends or younger people

Yes, you could, but the nuance is slightly different.

• 배추를 씻고 냄비에 넣고 국을 끓였어요
  = I washed the cabbage, put it in the pot, and made soup.

• 배추를 씻은 다음에 냄비에 넣고 국을 끓였어요
  = After washing the cabbage, I put it in the pot and made soup.

씻은 다음에 emphasizes the order a bit more clearly: first wash it, then do the next step.

So both are possible, but -은 다음에 sounds a little more explicitly sequential.

Yes. It sounds very much like a sequence of actions, such as describing what someone did while cooking.

The structure is:

1. 배추를 씻은 다음에 = after washing the cabbage
2. 냄비에 넣고 = put it in the pot
3. 국을 끓였어요 = made/cooked soup

This kind of chaining is extremely common in Korean when describing procedures, recipes, or past actions in order.