Na het koken wil Sofie de pan in de gootsteen spoelen.

Na het koken means after cooking or after the cooking is done.

A very common Dutch pattern is:

• na = after
• het + infinitive = a verbal idea used like a noun

So het koken literally works like the cooking, but in natural English we usually translate it as cooking.

Compare:

• Na het eten = after eating / after the meal
• Na het werken = after working
• Na het koken = after cooking

This is one of the standard ways Dutch turns a verb into something noun-like.

Because in this structure, the infinitive koken is being used as a noun-like expression, and Dutch normally uses het with it.

So:

• koken = to cook
• het koken = cooking / the act of cooking

After na, Dutch usually wants that noun-like form:

• na het koken
• na het lezen
• na het sporten

Na koken is not the normal standard form here.

This is because Dutch main clauses follow the verb-second rule.

The first position in the sentence is taken by Na het koken. Once that happens, the finite verb must come next:

• Na het koken | wil | Sofie | de pan in de gootsteen spoelen.

If you start with the subject, you get:

• Sofie wil de pan in de gootsteen spoelen na het koken.

Both are possible, but when Na het koken is moved to the front, wil must come before Sofie.

Because wil is a modal verb, and in Dutch main clauses the modal is the finite verb, while the other verb usually goes to the end.

So the structure is:

• wil = wants to
• spoelen = rinse

Together:

• Sofie wil ... spoelen = Sofie wants to rinse ...

This is very common with modal verbs:

• Ik kan Nederlands spreken. = I can speak Dutch.
• Zij moet vroeg vertrekken. = She must leave early.
• Wij willen de pan spoelen. = We want to rinse the pan.

Not exactly.

• spoelen usually means to rinse
• wassen means to wash
• afwassen often means to wash dishes or to do the washing-up

So de pan spoelen suggests rinsing the pan, probably with water, not necessarily thoroughly washing it with soap.

Depending on context:

• de pan wassen = wash the pan
• de pan afwassen = wash the pan as part of doing the dishes
• de pan spoelen = rinse the pan

Here in de gootsteen means in the sink, referring to the place where the rinsing happens.

Dutch often uses in for location:

• in de keuken = in the kitchen
• in de auto = in the car
• in de gootsteen = in the sink

So the idea is that Sofie wants to rinse the pan in the sink.

English might sometimes say rinse the pan in the sink or rinse the pan in/under the sink faucet, depending on context, but the Dutch sentence is perfectly natural as written.

Not necessarily.

Grammatically, Na het koken just means after cooking or after the cooking is done. The subject of koken is not explicitly stated.

In many real-life contexts, listeners will naturally assume it refers to Sofie or to whoever was cooking, but the sentence itself does not force that interpretation.

So it can mean:

• after Sofie has cooked
• after they have finished cooking
• after the cooking is done

Context tells you who did the cooking.

Because both nouns are de-words in Dutch:

• de pan = the pan
• de gootsteen = the sink

Dutch nouns are assigned either de or het. There is not always a logical reason you can predict from English, so learners usually have to memorize the article with the noun.

It is best to learn them as full units:

• de pan
• de gootsteen
• het fornuis
• de keuken

Yes. A few natural alternatives are possible, depending on emphasis:

• Sofie wil na het koken de pan in de gootsteen spoelen.
• Na het koken wil Sofie de pan afspoelen in de gootsteen.

These are slightly different in rhythm or nuance, but the original sentence is fully natural.

One small note:

• afspoelen often emphasizes rinsing off
• spoelen is also correct and understandable

So the original sentence is good Dutch, and other versions are mostly stylistic alternatives.