Hvis man glemmer den regel, kan der ske en ulykke.

Yes. Hvis is the normal word for if in a conditional sentence:

• Hvis man glemmer den regel ... = If one/you/people forget that rule ...

A useful comparison is:

• hvis = if in conditions
• om = usually whether / if in indirect questions

So here hvis is exactly the right choice.

Man is an impersonal pronoun. It often means:

• one
• you in a general sense
• people

So Hvis man glemmer den regel means something like:

• If one forgets that rule
• If you forget that rule
• If people forget that rule

In modern Danish, man is very common and natural. It does not sound as formal or old-fashioned as English one often does.

Because Hvis man glemmer den regel is a subordinate clause.

In Danish, subordinate clauses usually have subject + verb order:

• hvis man glemmer ...
• når hun kommer ...
• fordi de ved det ...

So after hvis, you normally say man glemmer, not glemmer man.

This is different from main clauses, where Danish follows the verb-second rule much more strongly.

Because the sentence begins with the hvis-clause, and that whole clause takes the first position in the sentence.

Danish main clauses normally put the finite verb in second position. So the structure is:

• Hvis man glemmer den regel = first position
• kan = second position

That gives:

• Hvis man glemmer den regel, kan der ske en ulykke.

If the sentence started directly with the main clause, you could say:

• Der kan ske en ulykke, hvis man glemmer den regel.

So both word orders are possible, but the position of kan changes because of Danish word-order rules.

Here der is an expletive or dummy word. It does not mean there as a place.

It is used in Danish in sentences that introduce the existence or occurrence of something:

• Der kommer en mand. = A man is coming / There comes a man.
• Der ligger en bog på bordet. = There is a book on the table.
• Der kan ske en ulykke. = An accident can happen.

So in this sentence, der helps build the construction there can happen an accident, even though natural English would usually just say an accident can happen.

Because kan is a modal verb, and after a modal verb Danish uses the infinitive of the next verb.

So:

• kan ske = can happen
• vil komme = will come
• skal gå = must go
• må vente = may / must wait

That is why you get:

• kan der ske en ulykke

not

• kan der sker en ulykke

Danish often uses the present tense in general conditions, just like English can:

• If you touch that, it burns.
• If people forget that rule, accidents can happen.

So Hvis man glemmer den regel expresses a general possibility or rule, not one specific past event.

Danish does not need a special verb form here. The present tense works naturally for general truths, warnings, and habitual possibilities.

This is an important difference.

• reglen = the rule
• den regel = that rule

In Danish, a noun by itself usually takes the definite ending:

• en regel = a rule
• reglen = the rule

But when you use den before a noun without an adjective, it is normally demonstrative:

• den regel = that rule

So this sentence is talking about a specific rule already known in the context: that rule.

Because the sentence is talking about an accident in general, not one specific accident already known to the listener.

• en ulykke = an accident
• ulykken = the accident

Here the meaning is: forgetting the rule may cause some accident / an accident. Since it is not a specific previously mentioned accident, Danish uses the indefinite form:

• en ulykke

Yes, in normal written Danish you put a comma after an initial subordinate clause like this:

• Hvis man glemmer den regel, kan der ske en ulykke.

The comma marks the end of the hvis-clause and the start of the main clause.

So this comma is standard and expected.