Hun kan tilgive sig selv, hvis hun ved, at hun gjorde sit bedste.

After a modal verb like kan (can), Danish uses the infinitive form of the main verb, without at.

So:

• hun kan tilgive = she can forgive
• not hun kan tilgiver

This works like:

• hun vil komme = she wants to come / she will come
• hun skal arbejde = she has to work
• hun må gå = she may / must go

So kan is the conjugated verb, and tilgive stays in the infinitive.

Yes. In a main clause, Danish normally follows the V2 rule: the finite verb comes in the second position.

Here the sentence begins with the subject:

• Hun = subject
• kan = finite verb

So the order is completely normal:

• Hun kan tilgive sig selv ...

If something else came first, the verb would still stay in second position:

• Hvis hun ved det, kan hun tilgive sig selv.

That verb-second pattern is very important in Danish main clauses.

Sig is the reflexive pronoun used for the third person when the object refers back to the subject of the clause.

So in:

• Hun kan tilgive sig selv

the person forgiving and the person being forgiven are the same person. That is why Danish uses sig.

Compare:

• Hun kan tilgive sig selv = She can forgive herself.
• Hun kan tilgive hende = She can forgive her.
  (some other woman)

Selv adds emphasis, like self in English. So sig selv = herself.

Sometimes sig can appear without selv, but with a verb like tilgive, sig selv is the natural and standard way to express forgive herself.

• Hun kan tilgive sig selv = natural
• Hun kan tilgive sig = possible in some contexts, but less standard/natural here

In many cases, selv makes it clear and idiomatic that the action turns back on the subject.

Yes. Hvis means if when introducing a condition:

• hvis hun ved ... = if she knows ...

This is the normal word for conditional if in Danish.

Do not confuse it with om, which can also sometimes translate as if, but usually in the sense of whether:

• Jeg ved ikke, om hun kommer. = I don’t know whether she is coming.

So here, because it is a condition, hvis is the right choice.

Here at is a conjunction meaning that.

• hun ved, at ... = she knows that ...

It introduces the clause that tells us what she knows.

So:

• hun ved = she knows
• at hun gjorde sit bedste = that she did her best

In English, that is sometimes omitted. In Danish, at is often kept and is very normal here.

Because the sentence describes:

• a present situation: she knows
• a past action: she did her best

So the logic is:

• hun ved = she knows now
• at hun gjorde sit bedste = that she did her best earlier

This is very natural in both Danish and English. The knowing happens in the present, while the doing happened in the past.

Both can be possible in Danish, but they are not exactly the same in feel.

• gjorde sit bedste = did her best
• har gjort sit bedste = has done her best

The version with gjorde presents the effort more simply as a past action. It often feels very natural when looking back on a completed situation.

The version with har gjort can put slightly more focus on the result or relevance to the present.

So:

• Hun kan tilgive sig selv, hvis hun ved, at hun gjorde sit bedste.
  is perfectly natural.

And so is:

• ... hvis hun ved, at hun har gjort sit bedste.

The original sentence just chooses the simple past.

This is because sin/sit/sine must agree with the gender/number of the noun they belong to.

In the fixed expression gøre sit bedste, the word bedste is treated like a neuter idea, similar to det bedste (the best thing / the best possible effort).

So we get:

• sit bedste

not:

• sin bedste

A useful way to think about it is that sit matches an implied neuter noun or the substantivized adjective bedste.

This expression is very common:

• Jeg gjorde mit bedste.
• Hun gjorde sit bedste.
• Vi gjorde vores bedste.

Sin/sit/sine are reflexive possessives. They refer back to the subject of the same clause.

In:

• hun gjorde sit bedste

the subject is hun, so the possessive that refers back to her is sit.

If you said hendes bedste, it would usually mean someone else’s best, not the subject’s own.

Compare:

• Hun gjorde sit bedste. = She did her best.
• Hun gjorde hendes bedste. = She did her best.
  This would usually sound wrong if hendes is meant to refer to hun. It suggests another female person.

So Danish strongly prefers sin/sit/sine when the possession refers back to the subject.

Because hvis and at introduce subordinate clauses, and subordinate clauses do not use main-clause V2 word order.

So Danish keeps the normal order:

• hvis hun ved
• at hun gjorde

not:

• hvis ved hun
• at gjorde hun

This is a major difference between main clauses and subordinate clauses in Danish.

Main clause:

• Hun kan tilgive sig selv.

Subordinate clause:

• hvis hun ved ...
• at hun gjorde ...

Because Danish normally uses commas to mark subordinate clauses.

So in:

• Hun kan tilgive sig selv, hvis hun ved, at hun gjorde sit bedste.

the commas show where the subordinate clauses begin:

• , hvis hun ved ...
• , at hun gjorde sit bedste

This is standard written Danish.

Yes. Gøre sit bedste is a very common expression meaning to do one’s best.

Examples:

• Jeg gjorde mit bedste. = I did my best.
• Han gør sit bedste. = He is doing his best.
• Vi vil gøre vores bedste. = We will do our best.

It is worth learning as a set phrase.

Yes. Danish can also put the conditional clause first:

• Hvis hun ved, at hun gjorde sit bedste, kan hun tilgive sig selv.

This means the same thing.

Notice what changes in the main clause after the initial subordinate clause:

• ... kan hun tilgive sig selv

The verb kan comes before the subject hun because the first position is already occupied by the hvis-clause. That is the V2 rule again.