Jeg tør ikke spørge læreren, hvis jeg ikke forstår spørgsmålet.

Tør is the present-tense form of turde, which means to dare.

So jeg tør ikke spørge means I don’t dare ask.

This verb behaves a lot like a modal verb in Danish, so it is often followed directly by another verb in the infinitive:

• Jeg tør ikke sige det.
• Han tør ikke gå ind.

Its forms are a bit irregular, which is why the present tense is tør rather than something more predictable like turder.

Because Danish main clauses normally follow V2 word order: the finite verb comes in the second position.

In Jeg tør ikke spørge læreren:

• Jeg = subject
• tør = finite verb
• ikke = negation
• spørge = infinitive

So the normal order is:

• Jeg tør ikke ...

This is similar to other Danish main clauses:

• Jeg kan ikke komme.
• Hun vil ikke vente.

The ikke usually comes after the finite verb in a main clause.

Because turde works like a modal verb here. After modal-type verbs in Danish, the next verb normally appears as a bare infinitive, without at.

So you get:

• Jeg tør spørge
• Jeg kan forstå
• Jeg vil gå
• Jeg skal læse

Not:

• Jeg tør at spørge (normally not used here)

So spørge is correct without at.

Those endings mark the definite form in Danish, which often corresponds to English the.

• en lærer = a teacher

• læreren = the teacher

• et spørgsmål = a question
• spørgsmålet = the question

So instead of putting a separate word like the before the noun, Danish often adds the definite ending to the noun itself.

This is one of the most important differences from English noun structure.

Here hvis means if in the sense of a condition.

The sentence means that the speaker does not dare ask the teacher in the situation where they do not understand the question.

Danish usually uses:

• hvis = if (conditional)
• om = whether / if (in indirect yes-no questions)

Compare:

• Jeg spørger læreren, hvis jeg ikke forstår spørgsmålet.
  = I ask the teacher if I don’t understand the question. (condition)

• Jeg spørger læreren, om spørgsmålet er vigtigt.
  = I ask the teacher whether the question is important.

So hvis is the right choice here because this is a condition, not a reported yes/no question.

Because a clause introduced by hvis is a subordinate clause, and subordinate clauses have different word order from main clauses.

In a subordinate clause, Danish usually puts ikke before the finite verb:

• hvis jeg ikke forstår
• fordi han ikke kommer
• at hun ikke ved det

Compare that with a main clause:

• Jeg forstår ikke spørgsmålet.
• Han kommer ikke.
• Hun ved det ikke.

So:

• main clause: jeg forstår ikke
• subordinate clause: hvis jeg ikke forstår

That difference is very common in Danish grammar.

Forstår is the present tense of forstå, which means to understand.

Typical forms are:

• at forstå = to understand
• forstår = understand / understands
• forstod = understood
• har forstået = have/has understood

In this sentence, jeg ikke forstår spørgsmålet means I do not understand the question.

Many Danish verbs form the present tense by adding -r:

• spørge → spørger
• forstå → forstår
• læse → læser

Because hvis jeg ikke forstår spørgsmålet is a subordinate clause, and Danish normally places a comma before subordinate clauses.

So the comma helps show the structure:

• main clause: Jeg tør ikke spørge læreren
• subordinate clause: hvis jeg ikke forstår spørgsmålet

This kind of comma is very common in written Danish.

Because spørge in Danish can take the person you ask as a direct object, just like English ask someone.

So:

• spørge læreren = ask the teacher
• spørge min ven = ask my friend

If you want to include the topic or thing asked about, Danish often uses om:

• Jeg spørger læreren om spørgsmålet.
• Hun spørger ham om vejen.

But in your sentence, læreren is simply the person being asked, so no preposition is needed.

Yes. Danish can put the subordinate clause first:

• Hvis jeg ikke forstår spørgsmålet, tør jeg ikke spørge læreren.

That is still correct, but the main clause changes word order because of the V2 rule:

• tør jeg ikke not
• jeg tør ikke

So when a different element comes first, the finite verb still has to stay in second position in the main clause.

That is why:

• Jeg tør ikke spørge læreren, hvis ... but
• Hvis ..., tør jeg ikke spørge læreren.