kono mondai ha sensei ni kikeba, sugu wakaru desyou.

聞けば is the -ba conditional form of 聞く (to ask / to hear).

• Dictionary form: 聞く
• Conditional form: 聞けば

It means if someone asks or if you ask in this sentence.

So:

• 先生に聞けば = if you ask the teacher

The -ba form often expresses a condition that leads naturally to a result. Here, the idea is:

• If you ask the teacher, you'll understand right away.

With 聞く when it means to ask someone, the person you ask is marked by に.

• 先生に聞く = ask the teacher

So に marks the target or person receiving the question.

Compare:

• 先生に聞く = ask the teacher
• 音楽を聞く = listen to music

The same verb 聞く can mean different things depending on context:

• ask someone
• listen to / hear something

In this sentence, because the target is 先生, it clearly means ask.

は marks 問題 as the topic: as for this problem...

So the sentence is structured like this:

• この問題は = as for this problem
• 先生に聞けば = if you ask the teacher
• すぐ分かるでしょう = you’ll probably understand right away

Even though 問題 is what is being understood, Japanese often makes it the topic rather than marking it as a direct object.

This is very natural in Japanese. English might focus on the subject more, but Japanese often starts by setting the topic first.

分かる is the most natural verb here because it means to understand or to become clear.

• 分かる = understand / know / become clear
• 知る = get to know / learn a fact
• 理解する = understand, but more formal or analytical

For a school problem, 分かる is very common and natural:

• この問題が分かる = understand this problem

In casual, everyday Japanese, learners will hear 分かる much more often than 理解する in sentences like this.

Japanese often leaves the subject unstated when it is obvious from context.

So this sentence does not literally specify who is asking or who will understand. Depending on context, it could mean:

• If you ask the teacher, you’ll understand right away.
• If we ask the teacher, we’ll understand right away.
• If one asks the teacher, it becomes clear right away.

In English, we usually need to choose a subject. In Japanese, leaving it out is very normal.

でしょう adds a sense like:

• probably
• I expect
• it will likely be the case
• sometimes a softer, less direct tone

So すぐ分かる is a plain statement:

• you’ll understand right away

But すぐ分かるでしょう sounds softer and slightly less absolute:

• you’ll probably understand right away
• I’m sure you’ll understand right away

It often reflects the speaker’s judgment or expectation rather than a blunt fact.

すぐ means immediately, right away, or soon.

In this sentence, it modifies 分かる:

• すぐ分かる = understand right away

It suggests that asking the teacher will quickly clear up the problem.

The comma is mainly for readability and to show a pause after the conditional clause.

• 先生に聞けば、すぐ分かるでしょう。

It separates:

1. the condition: if you ask the teacher
2. the result: you’ll probably understand right away

Japanese punctuation is often more flexible than English punctuation, so the comma is helpful but not always strictly required.

Yes, but the nuance changes a little.

• 先生に聞けば: if you ask the teacher, then you’ll understand
  
  • sounds like a general, natural condition
• 先生に聞いたら: if/when you ask the teacher
  
  • often a bit more conversational
• 先生に聞くと: when/if you ask the teacher
  
  • can sound more like a general consequence or automatic result

In this sentence, 聞けば is a very natural choice because it expresses a straightforward condition leading to a likely result.

この is a determiner that directly modifies a noun, so it goes straight before the noun:

• この問題 = this problem

You do not add の after この.

Compare:

• この本 = this book
• その先生 = that teacher
• あの学校 = that school over there

Words like この / その / あの must be followed by a noun.

Yes, it matters. 分かる behaves like an intransitive verb in Japanese.

That is why what is understood is often marked with が:

• この問題が分かる = understand this problem

But in your sentence, この問題 is the topic, so it uses は instead:

• この問題は…分かる

This is one reason 分かる can feel different from English understand, which takes a direct object:

• English: I understand this problem
• Japanese: more literally, As for this problem, it becomes understandable / is understandable

That difference is very common and important for learners.