joreop hueneun eotteon ireul hago sipeoyo?

The sentence breaks down like this:

• 졸업 후에는 = after graduation / as for after graduation
• 어떤 일을 = what kind of work/job
• 하고 싶어요 = want to do

So the structure is:

time/topic + object + verb

That is very normal in Korean. The main verb comes at the end, and the thing being asked about appears before it.

후 means after.

• 후에 = after
• 후에는 = after + as for / in the case of

Here is the breakdown:

• 후 = after
• 에 = at/in/after, marking the time point
• 는 = topic marker

So 졸업 후에는 means something like as for after graduation or after graduation, ...

The 는 adds a slight topic or contrast feeling. It can sound like:

• When it comes to after graduation...
• As for what happens after graduation...

If you remove 는 and say 졸업 후에, the sentence is still natural. It just sounds a little more neutral.

Both are possible, but they work a little differently.

• 졸업 후 = after graduation
• 졸업한 후(에) = after graduating

In 졸업 후, 졸업 is being treated like a noun meaning graduation.

In 졸업한 후, 졸업하다 is treated as a verb, and 졸업한 modifies 후.

So:

• 졸업 후에는 어떤 일을 하고 싶어요? = very natural, concise
• 졸업한 후에는 어떤 일을 하고 싶어요? = also natural, slightly more explicitly verbal

Korean often uses these compact noun-based expressions.

어떤 means what kind of or which kind of.

So 어떤 일 means:

• what kind of work
• what kind of job
• what sort of thing you want to do as work

It asks about the type or nature of the work, not just a yes/no answer.

Both can often be translated as what kind of work or what job, and in many situations both are natural.

A rough difference is:

• 어떤 일 = what kind of work / what sort of work
  
  • can sound a bit broader or more about the nature/type
• 무슨 일 = what work / what job
  
  • very common in everyday Korean

In this sentence, 어떤 일 sounds like asking about the kind of career or work someone hopes to do after graduation.

을/를 is the object marker.

Here:

• 일 = work, job
• 일을 = work/job as the object of the verb

The verb phrase is 일을 하다, literally to do work.

So:

• 어떤 일을 하고 싶어요? = What kind of work do you want to do?

In casual spoken Korean, 을/를 is sometimes dropped, but in a standard textbook-style sentence it is usually kept.

Because -고 싶다 is a grammar pattern that attaches to the verb stem.

The verb is 하다.

• verb stem: 하-
• add -고 싶어요
• result: 하고 싶어요

This pattern means want to do.

More examples:

• 먹고 싶어요 = want to eat
• 가고 싶어요 = want to go
• 배우고 싶어요 = want to learn

So 하고 싶어요 is the correct form.

싶어요 is the polite informal style, often called 해요체.

It is polite and very common in conversation.

Related forms:

• 싶어 = casual, plain conversational
• 싶어요 = polite everyday speech
• 싶습니다 = more formal

So this sentence is polite and natural for normal conversation, like speaking to a teacher, classmate you are being polite with, or someone you do not know very closely.

Yes, the subject is omitted.

Korean often leaves out subjects and objects when they are clear from context. In a question like this, it is understood that the speaker is asking you.

So even though you does not appear explicitly, the meaning is naturally:

What kind of work do you want to do after graduation?

If you added you, it would usually be unnecessary and sometimes less natural.

It can mean either, depending on context, but it often sounds fairly broad.

어떤 일을 하다 usually refers to:

• what kind of work you want to do
• what field you want to work in
• what sort of career you want

So the question could invite answers like:

• 선생님이 되고 싶어요. = I want to become a teacher.
• IT 회사에서 일하고 싶어요. = I want to work at an IT company.
• 디자인 관련 일을 하고 싶어요. = I want to do design-related work.

It is not limited to a single job title.

Yes, absolutely.

• 졸업 후에는 어떤 일을 하고 싶어요?
• 졸업 후에 어떤 일을 하고 싶어요?

Both are natural.

The version with 는 sounds a bit more like setting up after graduation as the topic:

• As for after graduation, what kind of work do you want to do?

The version without 는 is a little simpler and more neutral:

• What kind of work do you want to do after graduation?

Because Korean is generally an SOV language: subject-object-verb.

English usually follows SVO:

• You want to do what kind of work?

Korean puts the main verb at the end:

• 어떤 일을 하고 싶어요

This is one of the biggest structural differences for English speakers. In Korean, you often need to wait until the end to get the full action or meaning.

It sounds completely natural.

It is a very normal question to ask:

• in class
• in an interview practice situation
• when talking about future plans
• when getting to know someone

It is polite, clear, and common. The only thing that changes in real conversation is that people might use slightly different wording depending on tone, such as:

• 졸업 후에 뭐 하고 싶어요? = What do you want to do after graduation?
• 졸업하고 나서 무슨 일 하고 싶어요? = What kind of work do you want to do after you graduate?

But your original sentence is fully natural.