kono mondai ha muzukasikute, nakanaka kotae ga wakarimasen.

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

So the sentence is structured like:

• この問題は = As for this problem / This problem
• 難しくて、なかなか答えが分かりません = it is difficult, and I can’t easily figure out the answer

Using は does not just label the subject mechanically; it sets up what the speaker is talking about.

難しい is an i-adjective, and its て-form is made by changing -い to -くて:

• 難しい → 難しくて

The て-form connects this adjective to what follows. Here it means something like:

• it’s difficult, and so...
• because it’s difficult...

So:

• この問題は難しくて、なかなか答えが分かりません。 = This problem is difficult, so I can’t easily figure out the answer.

It can feel like either, depending on context.

The て-form often links ideas in a flexible way. In this sentence, the most natural interpretation is reason/cause:

• It’s difficult, so / because of that, I can’t figure out the answer.

A very literal and is possible grammatically, but in real usage the listener usually understands a causal connection.

With a negative verb, なかなか usually means:

• not easily
• not readily
• not for quite a while

So:

• なかなか答えが分かりません = I can’t easily figure out the answer = I’m having a hard time figuring out the answer

It adds the nuance that the answer does not come to you quickly or smoothly.

Yes. Its meaning changes depending on whether the sentence is positive or negative.

• なかなか + negative
  = not easily / not readily
  Example: なかなか寝られない。
  I can’t fall asleep easily.

• なかなか + positive
  = quite / pretty / unexpectedly very
  Example: なかなか面白い。
  It’s quite interesting.

In your sentence, because the verb is negative (分かりません), なかなか means not easily.

Because 分かる usually takes the thing understood with が, not を.

So in Japanese, the thing that becomes clear or understandable is marked with が:

• 答えが分かる = to understand / know the answer
• 日本語が分かる = to understand Japanese

Even though English uses understand + object, Japanese uses a different pattern here.

So:

• 答えが分かりません = I don’t know / understand the answer

分かる and 知る are related but different.

• 分かる = to understand, to figure out, to become clear
• 知る / 知っている = to know, to be aware of, to have knowledge of

In this sentence, the speaker is struggling to figure out the answer to a problem. That is why 分かりません is natural.

• 答えが分かりません = I can’t tell what the answer is / I don’t understand the answer
• 答えを知りません = I do not know the answer
  This sounds more like you simply lack the information.

Because the problem is difficult, 分かりません fits better.

Not exactly.

• 答えが分かりません = I can’t figure out the answer
• 解けません = I can’t solve it

They are close, but the focus is a little different:

• 答えが分かりません focuses on the answer not becoming clear
• 解けません focuses on being unable to solve the problem

For many situations, both could make sense, but they are not identical.

Japanese often omits subjects when they are understood from context.

So this sentence does not explicitly say I, but the natural understanding is usually:

• I can’t figure out the answer

Depending on context, it could also mean we or even be a more general statement, but in everyday use it usually refers to the speaker.

This omission is very common in Japanese.

The verb ends in -ます form:

• 分かる → 分かります
• negative: 分かりません

This makes the sentence polite and neutral.

A plain version would be:

• この問題は難しくて、なかなか答えが分からない。

That would sound more casual.

The dictionary form is 分かる.

Here is the breakdown:

• dictionary form: 分かる
• polite form: 分かります
• polite negative: 分かりません

So 分かりません means do not understand / cannot tell / do not know in a polite style.

この means this and must be followed by a noun.

• この問題 = this problem

Compare:

• この = this + noun
• これ = this by itself

So you say:

• この問題 = this problem
• これは問題です = this is a problem

It is mostly a writing aid, not a grammar requirement.

The sentence could be written without it:

• この問題は難しくてなかなか答えが分かりません。

The comma just helps show a pause and makes the sentence easier to read.

They are usually added only for learners.

Normal Japanese is normally written without spaces:

• この問題は難しくて、なかなか答えが分かりません。

The spaced version is just to make the parts easier to see.

Yes. A natural English translation might be:

• This problem is difficult, and I can’t easily figure out the answer.
• This problem is hard, so I’m having trouble figuring out the answer.
• This question is difficult, and I just can’t work out the answer.

The exact English wording can vary, but the Japanese nuance is that the problem is difficult and the answer is not becoming clear.