sensei ha wakaranai mondai wo sinsetu ni setumeisite kuremasita.

は marks 先生 as the topic of the sentence: as for the teacher...

It does not just identify who did the action; it frames the sentence as being about the teacher. In English, we usually would not translate は directly, but its effect is something like:

• As for the teacher, ...
• The teacher, ...

You might also see 先生が in other contexts, but は is very natural here when the teacher is already known or being presented as the topic.

Because Japanese puts a modifying clause before the noun it modifies.

So:

• 分からない問題 = the problem(s) that I didn't understand = literally something like not-understood problem(s)

This is one of the most important differences from English. English uses a relative clause after the noun:

• the problems that I didn't understand

Japanese puts that whole idea before the noun:

• 分からない 問題

Japanese relative clauses do not use relative pronouns like that, which, or who.

So where English says:

• the problems that I didn't understand

Japanese simply says:

• 分からない問題

There is no extra linking word. The plain-form clause directly modifies the noun.

This is a very common question.

分からない is the plain non-past form, but in Japanese, a non-past form before a noun often describes a state or characteristic, not just strict present time.

So 分からない問題 means:

• problems that I don't understand
• or, in this past-context sentence, problems that I didn't understand at that time

Using 分からなかった問題 is also possible, but it sounds more explicitly tied to the past: problems that I did not understand.

So the difference is roughly:

• 分からない問題: problems that are/were not understandable to me
• 分からなかった問題: problems that I specifically did not understand at that past time

Both can work, but 分からない問題 is very natural.

Japanese often leaves out information that is obvious from context.

In 分からない問題, the person who does not understand is not stated, but it is usually understood to be:

• the speaker
• or the relevant person in context

So here, most learners would understand it as:

• the problems I didn't understand

Japanese does this all the time. If the context already makes it clear, pronouns like I, you, or he/she are often omitted.

を marks 問題 as the thing being explained.

So:

• 問題を説明する = to explain the problem(s)

That may feel a little different from English, because English sometimes focuses on the act of giving an explanation, but in Japanese 説明する commonly takes the thing explained as its object.

So here:

• 分からない問題を説明して = explain the problems I didn't understand

親切 means kindness or kind.

It is a na-adjective, and when you want to use a na-adjective adverbially, you usually add に.

So:

• 親切な先生 = a kind teacher
• 親切に説明する = to explain kindly

In this sentence, 親切に describes how the teacher explained the problems.

This is an important grammar point.

• 説明して = te-form of 説明する
• くれました = gave me/us the favor of doing

So 説明してくれました does not just mean explained. It means something like:

• explained for me
• went to the trouble of explaining to me
• kindly explained it to me/us

The verb くれる shows that the action was done for the speaker or the speaker's in-group, and it often carries a feeling of appreciation.

The difference is nuance.

• 説明しました = simply explained
• 説明してくれました = explained for me/us, with a sense that the speaker benefited from it

So くれました adds a feeling like:

• the teacher kindly did that for me
• I appreciate that the teacher explained it

Without くれる, the sentence is more neutral. With くれる, it sounds more personal and grateful.

Both are possible, but they differ in politeness and respect.

• くれました = polite, normal
• くださいました = more respectful/honorific

Because the person doing the action is a teacher, くださいました could be used if you want to sound more respectful toward the teacher.

So:

• 説明してくれました = normal polite narration
• 説明してくださいました = more respectful toward the teacher

The original sentence is still perfectly natural.

It could be either.

Japanese nouns usually do not show singular/plural the way English does. So 問題 can mean:

• a problem
• problems

You decide from context.

So this sentence could mean either:

• the problem I didn't understand
• the problems I didn't understand

Japanese usually places the main verb at the end, and modifiers come before what they modify.

So the sentence is built roughly like this:

• 先生は — as for the teacher
• 分からない問題を — the problem(s) I didn't understand
• 親切に — kindly
• 説明してくれました — explained for me

That is normal Japanese structure. A more literal English order would sound like:

• As for the teacher, the problems I didn't understand, kindly explained for me

Of course, natural English rearranges that into a more standard English sentence order.