Die polisiebeampte teken die saaknommer aan.

Because the full verb is aanteken, which is a separable verb in Afrikaans.

In a normal main clause:

• the conjugated verb part goes near the beginning: teken
• the separable particle goes to the end: aan

So:

• aanteken = to note down / record
• Die polisiebeampte teken die saaknommer aan.

This is very similar to separable verbs in Dutch and German.

If you use the infinitive, the parts stay together:

• om die saaknommer aan te teken

Here, teken ... aan means to note down, to record, or to enter officially.

That is important because teken by itself can have other meanings too, such as:

• to draw
• to sign

But in this sentence, because of aan, the meaning changes to record/write down officially.

So a learner should think of:

• teken = draw/sign
• aanteken = note down / record

Both nouns are definite here, so each one gets die:

• die polisiebeampte = the police officer
• die saaknommer = the case number

Afrikaans uses die as the definite article for:

• singular nouns
• plural nouns
• all genders

So unlike some other languages, you do not change the article for masculine, feminine, or neuter nouns.

Yes, die usually means the.

A very useful thing for English speakers is that Afrikaans articles are simpler than in many European languages:

• die = the
• ’n = a / an

Die does not change for gender, and it is also used with plurals.

Examples:

• die man = the man
• die vrou = the woman
• die kinders = the children

Yes. Afrikaans commonly writes compound nouns as one word.

So:

• polisie = police
• beampte = official / officer
• polisiebeampte = police officer

This is very normal in Afrikaans. English often uses two words where Afrikaans uses one compound word.

Yes, it is also a compound noun written as one word.

It is made from:

• saak = case
• nommer = number

So saaknommer literally means case number.

Again, this is a typical Afrikaans compound:

• English: case number
• Afrikaans: saaknommer

Because Afrikaans verbs usually do not change according to the subject in the present tense.

So you get:

• Ek teken
• Jy teken
• Hy teken
• Ons teken

This is much simpler than English, which has:

• I write
• he writes

In Afrikaans, the form usually stays the same.

The sentence follows the normal Afrikaans main-clause pattern:

Subject + finite verb + object + separable particle

So here:

• Die polisiebeampte = subject
• teken = finite verb
• die saaknommer = object
• aan = separable particle

That gives:

• Die polisiebeampte teken die saaknommer aan.

A native English speaker may expect the full verb together, but in Afrikaans separable verbs often split like this in main clauses.

Without aan, yes, it could suggest a different meaning, such as:

• drawing
• signing

That is why aan matters so much. It tells you that this is the verb aanteken, not just teken.

Compare:

• Hy teken. = He draws / signs.
• Hy teken dit aan. = He notes it down / records it.

In an infinitive construction, the separable verb comes back together as aan te teken.

For example:

• Die polisiebeampte moet die saaknommer aanteken.
• Dit is belangrik om die saaknommer aan te teken.

So:

• main clause: teken ... aan
• infinitive phrase: aan te teken or sometimes written together in dictionary form as aanteken

It is the thing being recorded, so it is the direct object.

Ask:

• What does the police officer record?

Answer:

• die saaknommer

So the action goes from the subject to that noun phrase:

• Die polisiebeampte records die saaknommer.

A few points may help:

• polisiebeampte is long because it is a compound word, but it is just the parts joined together.
• saak has a long aa sound.
• teken is roughly like tay-ken.
• aan has a long vowel sound, somewhat like ahn.

For many learners, the biggest issue is not pronunciation but recognizing that teken ... aan belongs together as one verb meaning.