Hun slog også kinden, så der kom et lille blåt mærke under øjet.

Slog is the past tense of slå.

The verb slå has several meanings depending on context, including hit, strike, beat, or bang. In this sentence, it means something like hit or banged.

So:

• slå = to hit
• slog = hit

In a normal Danish main clause, the finite verb usually comes early, and adverbs like også often come right after it.

So:

• Hun slog også kinden
• literally: She hit also the cheek
• natural English: She also hit her cheek

This placement is very common in Danish. English and Danish often place also differently.

Danish often uses the definite form of body parts when it is already clear whose body part is meant.

So:

• kinden = the cheek
• øjet = the eye

But in English, we usually translate these as her cheek and her eye because that sounds more natural in English.

This is very common with body parts in Danish. If the owner is obvious, Danish often avoids the possessive.

That is a very reasonable question, because learners often expect something like Hun slog sig på kinden.

The sentence as written is understandable, but many speakers would probably find Hun slog sig på kinden more natural if the meaning is that she hit her own cheek accidentally.

Compare:

• Hun slog kinden = she hit the cheek
• Hun slog sig på kinden = she hit herself on the cheek

So the original sentence is possible to understand, but it is slightly compact and may sound less natural than the reflexive version.

Here så means so or as a result.

It introduces the consequence of what happened before:

• Hun slog også kinden
• så der kom et lille blåt mærke under øjet

So the idea is:

• she hit her cheek
• and as a result, a small bruise appeared under her eye

Here der is not a location word. It is the same kind of there as in English sentences like:

• There was a problem
• There appeared a bruise

Danish often uses der when introducing something new into the sentence.

So:

• der kom et lille blåt mærke
• literally: there came a small blue mark
• natural English: a small bruise appeared or there was a small bruise

In Danish, kom is often used in a broader way than English came.

Here it means something like:

• appeared
• formed
• developed

So der kom et lille blåt mærke means that the bruise appeared after the impact.

This is a very natural Danish way to express that kind of result.

Blåt mærke is the normal Danish expression for a bruise.

Literally, it means blue mark, but you should usually learn it as a fixed expression:

• et blåt mærke = a bruise
• blå mærker = bruises

So even though the words are transparent, the full phrase works like one vocabulary item.

Because mærke is a neuter noun. You can see that from et mærke.

In Danish, adjectives often change form before a neuter singular noun:

• en blå bil
• et blåt mærke

So blå becomes blåt here.

By contrast, lille stays lille, because it is irregular and does not add -t in this pattern.

Because øjet is the definite form of øje.

The base noun is:

• et øje = an eye

The definite form is:

• øjet = the eye

And as mentioned earlier, Danish often uses the definite form with body parts when the owner is obvious. So under øjet naturally means under her eye in context.