houchou to manaita o katazuketa ato, nabe no naka no suupu o samashite oita.

Because 包丁とまな板 is treated as one combined noun phrase: knife and cutting board.

So the structure is:

包丁とまな板 + を + 片付けた

The particle と connects the two nouns, and then the whole group gets marked by を as the direct object of 片付けた.

あと means after here, and the verb before it is usually put in the plain past form when you mean after doing something.

So:

• 片付けたあと = after putting away / after tidying up

The past form does not mean the whole sentence is suddenly shifting to a different tense. It shows that the first action was completed before the next one happened.

A useful comparison:

• Vたあと = after doing V
• Vるまえ = before doing V

So 片付けたあと、… means after I put away the knife and cutting board, ...

Yes. あと is a noun meaning after / afterward / the time after.

That is why a verb in plain form can modify it, just like a relative clause modifies a noun:

• 片付けたあと = the time after putting away

This is a very common Japanese pattern:

• 食べたあと
• 帰ったあと
• 勉強したあと

Because the phrase is built in layers:

1. 鍋の中 = the inside of the pot
2. 鍋の中のスープ = the soup in the pot

So the first の connects pot and inside, and the second の connects inside of the pot to soup.

You can think of it as:

[鍋] の [中] の [スープ]
= [pot] 's [inside] 's [soup]
= more naturally, the soup inside the pot

Adding 鍋の中の specifies which soup we are talking about.

• スープを冷ましておいた = cooled the soup
• 鍋の中のスープを冷ましておいた = cooled the soup in the pot

So it gives a more concrete picture of the situation.

冷まして is the て-form of 冷ます.

• dictionary form: 冷ます
• て-form: 冷まして
• past: 冷ました

冷ます is a transitive verb, meaning to cool something.

So here:

• スープを冷まして = cooling the soup

This is different from 冷める, which is intransitive:

• スープが冷める = the soup cools / gets cold

Because 冷ます means someone intentionally cools something, while 冷める means something cools on its own.

In this sentence, the speaker is describing a deliberate action done to the soup, so 冷ます is the natural choice.

• 冷ます = to cool something
• 冷める = to become cool

Also, ～ておく often implies intentional preparation, so pairing it with the transitive verb 冷ます makes especially good sense.

～ておく often means one of these:

1. do something in advance
2. do something and leave it that way
3. do something for later convenience

So 冷ましておいた means more than just cooled. It suggests something like:

• cooled it ahead of time
• left it to cool / left it in a cooled state
• cooled it for later use

The exact nuance depends on context, but the key idea is intentional action with a later purpose or resulting state.

冷ました simply states the action:

• I cooled the soup.

冷ましておいた adds the nuance that the action was done in preparation, for later, or and then left that way:

• I cooled the soup and left it ready
• I had cooled the soup in advance

So ～ておく gives the sentence a more purposeful feeling.

It marks スープ as the direct object of 冷ます.

• スープを冷ます = to cool the soup

Since 冷ます is transitive, it normally takes を.

Yes.

The order is:

1. 包丁とまな板を片付けた
2. 鍋の中のスープを冷ましておいた

The phrase 片付けたあと makes it clear that putting away the knife and cutting board happened first, and cooling the soup happened afterward.

The subject is omitted because Japanese often leaves out information that is understood from context.

So the sentence does not explicitly say I, she, he, etc. A natural interpretation in isolation would often be I or someone being talked about.

This is very normal in Japanese. If the subject is obvious, it is usually not repeated.

Because this is a natural narrative-style sentence describing actions in sequence. Japanese does not need a topic marker in every sentence.

If the topic had already been established earlier, it would be easy to leave it out here.

For example, in a longer passage, you might already know that the speaker is talking about I, my mother, the cook, etc., so this sentence can simply present the actions without restating the topic.