Learn Dutch: Tijdens de repetitie was de regie van de monoloog erg moeilijk. - During the rehearsal the direction of the monologue was very difficult.

Because the sentence starts with the prepositional phrase Tijdens de repetitie (During the rehearsal). In Dutch, starting a main clause with anything other than the subject triggers inversion, meaning the finite verb and subject swap places.

The word repetitie looks like "repetition". Is that a correct translation?

It is a false friend in this context. While it stems from the same root, repetitie specifically means "rehearsal" in theater or music. If you want to say "repetition" (doing something again), you should use de herhaling.

Can I use regie for any kind of "direction"?

No, regie is strictly used for the artistic direction or management of a play, film, or project (the work done by a regisseur). For physical directions (like North or South), you would use de richting.

Is there a difference between using tijdens and gedurende in this sentence?

Both mean "during", but tijdens is the standard, most common choice in modern Dutch. Gedurende is more formal and often places extra emphasis on the fact that something lasted for the entire duration of the event (throughout the rehearsal).