Efter lokalbedøvelsen fylder tandlægen hullet og tjekker tandfyldningen.

This is because Danish follows the V2 rule in main clauses: the finite verb must come in the second position.

The sentence begins with the time phrase Efter lokalbedøvelsen = After the local anesthetic. Since that phrase takes the first position, the verb fylder must come next, and the subject tandlægen comes after it.

So the structure is:

Efter lokalbedøvelsen | fylder | tandlægen | hullet ...

If you started with the subject instead, you would get:

Tandlægen fylder hullet efter lokalbedøvelsen ...

That is also grammatical, but it gives a slightly different emphasis.

Lokalbedøvelse means local anesthetic / local anesthesia in the indefinite form.

Lokalbedøvelsen is the definite form, meaning the local anesthetic or the local anesthesia.

In Danish, definiteness is often shown by adding an ending to the noun instead of using a separate word like the:

• en lokalbedøvelse = a local anesthetic
• lokalbedøvelsen = the local anesthetic

Here, the sentence refers to a specific procedure already understood in the situation, so the definite form is natural.

Danish often forms new nouns by combining smaller words into compound nouns.

tandlægen comes from:

• tand = tooth
• læge = doctor
• tandlæge = dentist
• tandlægen = the dentist

So literally, it is something like tooth doctor. Writing compounds as one word is completely normal in Danish.

Because hul is a neuter noun in Danish:

• et hul = a hole
• hullet = the hole

Neuter nouns usually form the definite singular with -et.

Compare:

• en tandlæge → tandlægen
• et hul → hullet

So the ending depends on the noun’s gender.

For the same reason as lokalbedøvelsen and hullet: it refers to a specific thing in the situation, so Danish uses the definite form.

• en tandfyldning = a dental filling
• tandfyldningen = the dental filling

In this sentence, the dentist is checking the filling that was just placed, so the filling is the natural form.

They are two separate verbs joined by og = and:

• fylder hullet = fills the hole/cavity
• tjekker tandfyldningen = checks the filling

So the dentist does two actions:

1. fills the cavity
2. checks the filling

Also note that the subject tandlægen applies to both verbs, even though it is only said once.

Again, this is a Danish compound noun.

It is made from:

• tand = tooth
• fyldning = filling

Together:

• tandfyldning = dental filling / tooth filling

Danish uses compounds very freely, much more than English in some cases. So learners should get used to seeing long nouns built from smaller parts.

Yes. In everyday Danish, hul literally means hole, but in dental contexts it can naturally refer to a cavity.

So in this sentence:

• hullet literally = the hole
• but in natural English it may be translated as the cavity

This is very common when translating: the most literal meaning is not always the most natural one in context.

Because Danish, like English, can omit the repeated subject when two verbs share the same subject and are connected by og.

So:

Efter lokalbedøvelsen fylder tandlægen hullet og tjekker tandfyldningen.

means:

After the local anesthetic, the dentist fills the cavity and checks the filling.

You could repeat the subject, but it would sound unnecessary:

... fylder tandlægen hullet, og tandlægen tjekker tandfyldningen.

That is grammatical, but much less natural.

Yes, tjekke is a normal and very common Danish verb, borrowed from English check.

• at tjekke = to check
• tjekker = checks / is checking

Danish has many everyday borrowed words like this, especially in informal or practical language. In some contexts, you might also see more formal alternatives such as kontrollere, but tjekke is very natural here.