zatuon ga sukunai to, sensei no nihongo ga yoku kikitoreru.

Because 少ない is the plain form of an い-adjective, and the conditional と attaches to the plain form.

So:

• 雑音が少ない = there is little noise / the noise is low
• 雑音が少ないと = if/when there is little noise

By contrast:

• 少なく is the adverbial form, so it needs something after it, such as 少なくなる or 少なくて

Also, 少ない is one of those words that often works like this:

• お金が少ない = there is little money
• 時間が少ない = there is little time
• 雑音が少ない = there is little noise

So even though English might use something like little noise, Japanese expresses it as noise is few/little.

Here, が marks 雑音 as the subject of the conditional clause:

• 雑音が少ない = the noise is low / there is little noise

Using が sounds neutral and descriptive. It simply presents the condition.

If you used は instead:

• 雑音は少ないと、...

that would sound unusual here, because は introduces a topic or contrast, and this sentence is not really trying to contrast noise with something else.

In short:

• が = natural for stating the condition plainly
• は = would add contrast or topical emphasis

Here, と is a conditional, meaning something like:

• if
• when
• whenever

So:

• 雑音が少ないと、先生の日本語がよく聞き取れる。
• If/When there is little noise, I can hear the teacher’s Japanese well.

This と often expresses a natural result, general truth, or regular outcome.

So the nuance is not just a random hypothetical. It sounds more like:

• whenever the noise level is low, the result is that the teacher’s Japanese is easy to catch

That is why と fits well here.

Yes, but the nuance changes.

• 雑音が少ないと、先生の日本語がよく聞き取れる。
  This sounds like a general or predictable result.

• 雑音が少なかったら、先生の日本語がよく聞き取れる。
  This sounds more like a specific hypothetical situation: if the noise were low...

• 雑音が少ないなら、先生の日本語がよく聞き取れる。
  This sounds more like if it is the case that the noise is low... and can feel a bit more contextual or conversational.

So と is the best choice if the speaker means a regular cause-and-effect relationship.

先生の日本語 literally means the teacher’s Japanese, but in this sentence it most naturally means:

• the Japanese the teacher is speaking
• the teacher’s Japanese speech
• what the teacher says in Japanese

The particle の does not only show ownership. It can show many kinds of relationships.

So here it is not necessarily talking about the teacher’s Japanese ability in an abstract sense. It is more about the Japanese coming from the teacher that the listener is trying to understand.

Because with ability or potential expressions in Japanese, the thing that can be done is often marked with が.

Here:

• 聞き取れる = can make out / can catch what is being said
• 先生の日本語が聞き取れる = the teacher’s Japanese can be made out

This is very common with potential forms:

• 日本語が話せる = can speak Japanese
• 漢字が読める = can read kanji
• 先生の日本語が聞き取れる = can catch the teacher’s Japanese

So the second が is not strange once you think of 聞き取れる as an ability expression.

聞き取れる is the potential form of 聞き取る.

• 聞く = to hear / to listen / to ask
• 聞き取る = to catch what is said, to make out, to perceive clearly
• 聞き取れる = can catch what is said, can make out

So this sentence is not just saying that the teacher’s voice reaches your ears. It means you can successfully identify and understand the spoken sounds.

That makes 聞き取れる a very good word for situations involving:

• noise
• unclear pronunciation
• fast speech
• listening comprehension

These are related, but they are not the same.

聞こえる

• means something like is audible or can be heard
• focuses on sound reaching your ears

Example nuance:

• 先生の声が聞こえる = I can hear the teacher’s voice

聞ける

• potential form of 聞く
• can mean can listen or have the chance/ability to hear
• does not necessarily mean you can clearly make out every word

Example nuance:

• 先生の話が聞ける = I can listen to the teacher’s talk

聞き取れる

• means can make out, can catch, can understand what is being said by listening
• focuses on successful auditory comprehension

So in this sentence, 聞き取れる is the best choice because the problem is not just whether sound exists, but whether the speech can be clearly caught through the noise.

Here, よく means well, not often.

So:

• よく聞き取れる = can hear clearly / can make out well

Japanese よく can mean different things depending on context:

• よく行く = go often
• よく分かる = understand well
• よく見える = can see clearly
• よく聞き取れる = can hear clearly / can make out well

In this sentence, because it modifies an ability verb about hearing, well/clearly is the natural meaning.

Sometimes, in modern Japanese, you may hear を used with potential forms, especially in casual speech. But in standard textbook-style Japanese, が is the safer and more typical choice.

So:

• 先生の日本語が聞き取れる = standard and very natural
• 先生の日本語を聞き取れる = possible in some usage, but less standard in careful grammar teaching

For learners, it is best to remember:

• with potential forms, use が first

That will sound correct in most situations.

It sounds more like a general fact or regular result.

Because of と, the sentence has the feel of:

• whenever the noise is low, the teacher’s Japanese is easy to catch
• low noise leads to better listening comprehension

If the speaker wanted to talk about one particular future or imagined situation, たら would often sound more natural.

So this sentence feels like a general observation about listening conditions.