seonsaengnim seolmyeongeul deutgo naseo i munjereul ihaehaesseoyo.

Korean usually puts the verb at the end of each clause.

So this sentence is built like:

• 선생님 설명을 = the teacher’s explanation
• 듣고 나서 = after listening
• 이 문제를 = this problem/question
• 이해했어요 = understood

A very literal English order would be:

• Teacher explanation listened-to after, this problem understood.

That sounds unnatural in English, but it is normal in Korean. A good habit is to look for the final verb first, then work backward.

Both are possible.

• 선생님 설명 = teacher explanation
• 선생님의 설명 = the teacher’s explanation

In Korean, the possessive marker -의 is often omitted when the relationship is obvious. So 선생님 설명 sounds natural and common in everyday speech.

Using 선생님의 설명 would be a little more explicit, but not necessary here.

The particle -을/를 marks the object of the verb.

Here, the verb is 듣다 (to listen to / hear), so:

• 설명 = explanation
• 설명을 듣다 = to listen to the explanation

So 설명을 tells you that explanation is what was listened to.

듣고 나서 means after listening or after having listened.

It is made from:

• 듣다 = to listen
• 듣고 = listen and...
• 나서 = after doing that

Together, V-고 나서 means:

• after doing V
• often with the sense that the first action is completed before the next one happens

So 설명을 듣고 나서 means after listening to the explanation.

Good question. Both can connect actions, but the nuance is different.

• 듣고 이해했어요 = listened and understood
• 듣고 나서 이해했어요 = understood after listening

-고 can simply connect two actions in sequence. -고 나서 emphasizes that the first action happened first, and then the second happened after that.

So in this sentence, -고 나서 makes the time order especially clear.

이해하다 is the dictionary form meaning to understand.

It is made of:

• 이해 = understanding
• 하다 = to do

When you conjugate it in polite past tense:

• 이해하다 → 이해했어요

This is just the normal past polite form.

So:

• 이해해요 = understand / am understanding
• 이해했어요 = understood

Because 이해하다 means to understand, while 알다 usually means to know.

Compare:

• 알다 = to know a fact, person, method, answer, etc.
• 이해하다 = to understand something in a meaningful way

In this sentence, the idea is that after hearing the teacher’s explanation, the speaker came to understand the problem. So 이해하다 is the natural choice.

It can mean either, depending on context.

• 문제 can mean problem
• It can also mean question on a test, worksheet, or exercise

So if this sentence is about math homework, it might be this problem. If it is about an exam item, it might be this question.

Both are possible translations.

Korean often omits the subject when it is clear from context.

So even though English usually needs I, Korean does not have to say 저는 or 나는 here.

The sentence naturally implies:

• (I) understood this problem after listening to the teacher’s explanation.

If needed for emphasis or clarity, you could say:

• 저는 선생님 설명을 듣고 나서 이 문제를 이해했어요.

But in normal conversation, leaving it out is very common.

이해했어요 is in the polite informal style, often called 해요체.

It is polite and very common in everyday speech.

Compare:

• 이해했어요 = polite
• 이해했습니다 = more formal
• 이해했어 = casual, used with close friends or younger people

So this sentence sounds polite and natural in many normal situations.

Yes, that is also correct.

Compare:

• 듣고 나서 = after listening
• 들은 후에 = after having listened / after listening

Both express sequence. However:

• -고 나서 is very common and conversational
• -은 후에 can sound a bit more formal or written

So your original sentence sounds very natural in speech.

Because 듣다 is an irregular verb.

Its stem is 듣-, but when a vowel-like ending is added, the ㄷ changes to ㄹ.

So:

• 듣다
• 들어요
• 들으면
• 듣고 ← here it stays 듣고, not 들고

This part can be confusing because not every form changes in the same way. The important thing is to memorize common forms:

• 듣다
• 들어요
• 들었어요
• 듣고

So 듣고 나서 is the correct form.

It strongly suggests that the teacher’s explanation led to the understanding, yes.

The sequence is:

1. listened to the explanation
2. then understood the problem

So the sentence naturally implies a connection between the two actions. It does not explicitly say only because of the explanation, but that is the most natural interpretation.