Anna zet haar boodschappentas in de bakfiets en wil daarna bij de slager afrekenen.

Because Anna is female, so Dutch uses haar for her.

• haar = her
• zijn = his

So:

• Anna zet haar boodschappentas... = Anna puts her shopping bag...

A useful note:

• haar can also mean hair in other contexts, but here it is clearly the possessive word her.

zet is the present tense of zetten, which often means to put, to place, or to set down.

In this sentence, zet is a natural choice because Anna is placing something somewhere:

• Anna zet haar boodschappentas in de bakfiets.
• Literally: Anna puts/places her shopping bag into the cargo bike.

Why not doet?

Dutch doen can also sometimes be used for putting something somewhere, especially in speech:

• Ze doet de tas in de bakfiets.

That is possible, but zetten sounds a bit more specific and deliberate here, especially because a bag is being placed into something.

Yes. Dutch very often combines nouns into one word.

boodschappentas = boodschap + tas

More exactly in meaning:

• boodschappen = groceries / shopping
• tas = bag

So boodschappentas means:

• shopping bag
• grocery bag

This is very normal in Dutch. Compare:

• fietsbel = bicycle bell
• huisdeur = front door / house door
• schooltas = school bag

English often uses separate words, but Dutch usually writes these combinations as one word.

A bakfiets is a very Dutch kind of bicycle with a large box or container for carrying things, children, groceries, etc.

• bak = box / container / tray
• fiets = bicycle

So a bakfiets is often translated as:

• cargo bike
• box bike

In this sentence, Anna is putting her shopping bag into the cargo bike.

Because the bag is being placed inside the box/container part of the cargo bike.

• in = in / inside
• op = on / on top of

So:

• in de bakfiets = in the cargo bike, meaning inside its cargo box
• op de bakfiets would suggest on top of the bike, which is not the intended meaning here

Dutch often uses in when something goes into a container or enclosed space.

Because Dutch, like English, can omit the subject in the second clause when it is the same as in the first clause.

The full version could be:

• Anna zet haar boodschappentas in de bakfiets en Anna wil daarna bij de slager afrekenen.

But repeating Anna sounds unnecessary, so Dutch normally leaves it out:

• Anna zet haar boodschappentas in de bakfiets en wil daarna bij de slager afrekenen.

This works because the subject of both actions is clearly the same person: Anna.

Both are possible, but they are structured slightly differently.

In the sentence you have:

• ... en wil daarna bij de slager afrekenen.

Here, after en, the subject is omitted because it is the same as before, so wil comes immediately.

You could also say:

• ... en wil daarna bij de slager afrekenen.
• ... en daarna wil ze bij de slager afrekenen.
• ... en daarna wil Anna bij de slager afrekenen.

If you include daarna first, then normally you also include the subject after the verb:

• Daarna wil ze...

The version in your sentence is very natural and compact.

daarna means:

• after that
• afterwards
• then

In this sentence:

• Anna zet haar boodschappentas in de bakfiets en wil daarna bij de slager afrekenen.
• Meaning: she first puts the bag in the cargo bike, and after that she wants to pay at the butcher’s.

Possible positions for daarna depend on sentence structure, for example:

• Anna wil daarna afrekenen.
• Daarna wil Anna afrekenen.
• Ze wil daarna bij de slager afrekenen.

So daarna is a flexible time adverb, much like afterwards in English.

Literally, bij de slager means at the butcher.

In Dutch, this can refer to:

• the butcher as a person
• the butcher’s shop

Very often, it effectively means at the butcher’s shop, just like English at the butcher’s.

Examples:

• Ik koop vlees bij de slager. = I buy meat at the butcher’s.
• Ze rekent af bij de slager. = She pays at the butcher’s.

So in this sentence, it most naturally means Anna wants to pay at the butcher’s shop.

afrekenen is a separable verb.

It consists of:

• af
• rekenen

The basic meaning here is:

• to pay
• to settle the bill
• to check out

In Dutch, separable verbs behave differently depending on the sentence.

In a simple main clause:

• Anna rekent af. = Anna pays / settles up.

Here the verb splits:

• rekent goes in the normal verb position
• af goes toward the end

But after a modal verb like wil, the whole infinitive stays together at the end:

• Anna wil afrekenen. = Anna wants to pay.

That is exactly what happens here:

• ... wil daarna bij de slager afrekenen.

Because after a modal verb like willen, Dutch uses the infinitive without te.

So:

• wil afrekenen = wants to pay

Not:

• wil te afrekenen ❌

Common modal verbs that behave this way include:

• willen = to want
• kunnen = can / to be able to
• mogen = may / to be allowed to
• moeten = must / to have to
• zullen = shall / will
• gaan can also act similarly in near-future constructions

Examples:

• Ik wil eten. = I want to eat.
• Ze kan komen. = She can come.
• Wij moeten betalen. = We must pay.

Because both bakfiets and slager are de-words in Dutch.

Dutch nouns usually take either:

• de
• het

Unfortunately, this often has to be learned noun by noun.

Here:

• de bakfiets
• de slager

A few helpful patterns:

• nouns referring to people are very often de-words, so de slager is not surprising
• many everyday objects are also de-words, but this is less predictable

So it is best to learn the noun together with its article:

• de bakfiets
• de slager
• de boodschappentas

Yes, wil is the present tense of willen for hij/zij/het and also often for singular subjects like Anna.

Conjugation of willen in the present tense:

• ik wil
• jij wilt / wil
• hij wil
• zij wil
• wij willen
• jullie willen
• zij willen

Because Anna is a third-person singular subject, we use:

• Anna wil...

Not:

• Anna wilt... ❌

Yes. In many contexts, afrekenen means:

• to pay
• to settle the bill
• to check out

But in other contexts it can also mean something like:

• to settle scores
• to deal with decisively

For example:

• Ik moet nog afrekenen in de winkel. = I still need to pay in the shop.
• Hij wil afrekenen met zijn verleden. = He wants to settle accounts with his past.

In your sentence, because of bij de slager, it clearly means to pay.

Yes, that is a good natural translation in many contexts.

Depending on tone, you could translate it as:

• to pay at the butcher’s
• to settle the bill at the butcher’s
• to check out at the butcher’s

The most direct and neutral option is usually:

• to pay at the butcher’s

So the whole second part:

• wil daarna bij de slager afrekenen can be understood as:
• wants to pay at the butcher’s afterwards

It sounds normal and natural, though slightly neat and textbook-like because it is very clear and complete.

Nothing in it is unusually formal:

• zet is normal
• boodschappentas is normal
• bakfiets is common in the Netherlands
• bij de slager afrekenen is standard everyday Dutch

A more casual spoken version might use slightly simpler wording, for example:

• Anna doet haar boodschappentas in de bakfiets en wil daarna bij de slager betalen.

But the original sentence is absolutely normal Dutch.