Hun er klog nok til at forstå det.

Here nok means enough.

So klog nok = smart enough.

Be careful: nok can also mean probably in other sentences, but not here.

• Hun er klog nok til at forstå det. = She is smart enough to understand it.
• Hun er nok klog. = She is probably smart.

So the position of nok matters a lot.

In Danish, when nok means enough, it normally comes after the adjective or adverb.

So:

• klog nok = smart enough
• gammel nok = old enough
• hurtigt nok = fast enough

This is different from English, where enough also comes after the adjective:

• smart enough
• old enough
• fast enough

So this part actually works very similarly in Danish and English.

Til at + infinitive is a very common Danish pattern after nok.

The structure is:

adjective + nok + til at + infinitive

So:

• klog nok til at forstå det = smart enough to understand it

You can think of til at here as the Danish way of linking enough with the action that follows.

More examples:

• Han er gammel nok til at køre bil. = He is old enough to drive.
• Jeg er stærk nok til at løfte den. = I am strong enough to lift it.

Because forstå is an infinitive here, and Danish normally uses at before the infinitive in this kind of construction.

So:

• at forstå = to understand

In this sentence, til at forstå is the full phrase required by the pattern.

Compare:

• Hun prøver at forstå det. = She tries to understand it.
• Hun er klog nok til at forstå det. = She is smart enough to understand it.

Danish does sometimes omit at after certain verbs, but not in this structure.

Because klog is agreeing with hun, and here the basic form is used.

With predicate adjectives after er, Danish often shows agreement like this:

• Hun er klog.
• Han er klog.
• Den er klog.

But:

• Det er klogt.

So the -t form is typically used with det or another neuter singular noun.

Examples:

• Et barn er klogt. = A child is clever.
• En pige er klog. = A girl is clever.

Since hun refers to a person and corresponds to common gender, klog is correct here.

Det here means it or that, depending on context.

It refers to whatever is being understood. The exact meaning depends on the situation.

For example:

• if people are discussing a problem, det might mean the problem
• if someone explained something, det might mean the explanation
• if it refers to a statement, det might mean that

So forstå det simply means understand it/that.

The word order is very normal for a Danish main clause:

Hun | er | klog nok | til at forstå det

• Hun = subject
• er = finite verb
• klog nok = complement
• til at forstå det = infinitive phrase

This is a standard declarative sentence.

Also remember that Danish is a V2 language, which means the finite verb is normally in the second position in main clauses. Here that happens naturally because the subject comes first:

• Hun er klog nok til at forstå det.

If something else comes first, the verb still stays second:

• I dag er hun klog nok til at forstå det. = Today she is smart enough to understand it.

You could, but it means something different.

• Hun er klog nok til at forstå det. = She is smart enough to understand it.
• Hun er nok klog til at forstå det. = She is probably smart enough / smart enough, I suppose, to understand it.

In the second sentence, nok is no longer part of klog nok. Instead, it acts more like a sentence adverb meaning probably.

So if you want enough, keep nok directly after the adjective:

• klog nok

Yes, very often. This is a very productive pattern in Danish.

Pattern:

[subject] + er + adjective + nok + til at + infinitive

Examples:

• Han er stærk nok til at bære den. = He is strong enough to carry it.
• Du er gammel nok til at bestemme selv. = You are old enough to decide for yourself.
• Vi er heldige nok til at have gode naboer. = We are lucky enough to have good neighbors.

So once you learn klog nok til at, you can reuse the same structure with many other adjectives.

In normal speech, it is a very natural sentence.

A few useful pronunciation notes:

• Hun is pronounced roughly like hoon, but with a Danish u sound.
• er is often weak and short in speech.
• nok has a short vowel.
• at is often pronounced very weakly, almost like å in connected speech.
• det is often pronounced weakly too, especially at the end.

So in fluent speech, til at forstå det may sound more connected and reduced than the spelling suggests.

The sentence is completely normal and idiomatic in everyday Danish.