sensei no setumei wo kikinagara, daizina pointo wo memosimasu.

Because there are two separate verb-object pairs:

• 先生の説明を聞きながら = listen to the teacher’s explanation
• 大事なポイントをメモします = take notes on the important points

In Japanese, each verb can have its own direct object, so using を twice is completely normal here.

ながら means while doing or as someone does.

So:

• 聞きながら = while listening

It connects two actions done at the same time. In this sentence, the speaker is:

• listening to the teacher’s explanation
• and taking notes at the same time

A useful nuance: with Aながら、B, the B action is usually the main action of the sentence.

Because ながら attaches to the verb stem (the ます-stem), not the dictionary form.

Examples:

• 聞く → 聞きます → 聞きながら
• 食べる → 食べます → 食べながら
• 読む → 読みます → 読みながら

So 聞きながら is the correct form.

Here の links two nouns and shows a relationship between them.

• 先生 = teacher
• 説明 = explanation
• 先生の説明 = the teacher’s explanation

You can think of it as the explanation by the teacher or the teacher’s explanation. It does not always mean literal possession; it often just connects related nouns.

Because 大事 is a na-adjective, not an i-adjective.

When a na-adjective directly modifies a noun, you add な:

• 大事なポイント = important points

Compare:

• 大きいポイント = a big point (i-adjective)
• 大事なポイント = an important point (na-adjective)

So the な is required before the noun.

メモします means to make a note, to jot down, or to take notes.

It is related to the noun メモ = memo/note.
So ポイントをメモします means something like:

• I note down the key points
• I take notes on the important points

書きます just means write, which is broader.
メモします specifically suggests note-taking.

Japanese often omits the topic or subject when it is clear from context.

So this sentence could be understood as:

• (私は) 先生の説明を聞きながら、大事なポイントをメモします。

The 私は is simply left out because it is not necessary. This is very common in natural Japanese.

It comes from English, but in Japanese ポイント often means:

• key point
• main point
• important part

So 大事なポイント is very natural Japanese for important points or key points.

Loanwords in Japanese often have meanings that are similar to English, but their usage can be a little narrower or more specialized.

The main action is メモします.

In a Verb-stem + ながら sentence, the ながら part gives a background action:

• 先生の説明を聞きながら = while listening to the teacher’s explanation

Then the final verb gives the main action:

• 大事なポイントをメモします = I take notes on the important points

So the sentence focuses most strongly on the note-taking, with listening happening alongside it.

Yes, but the original order is very natural.

Original:

• 先生の説明を聞きながら、大事なポイントをメモします。

This follows a common Japanese pattern:

• background/side action first
• main action last

You could sometimes rearrange parts for emphasis, but Japanese usually puts the main verb at the end, and this version sounds smooth and standard.

Both can relate to listening, but 聞く is the normal, general verb.

• 聞く = hear, listen, ask
• 聴く = listen attentively, especially to music or something carefully

For a teacher’s explanation, 聞く is the usual choice.
Using 聴く here would sound unusual to many learners, and 聞く is the safest standard form.