Min søster vil gerne deltage i kurset, hvis hun har tid om aftenen.

Because min/mit/mine must match the gender and number of the noun being possessed.

• min = common gender singular
• mit = neuter singular
• mine = plural

Søster is a common gender singular noun, so the correct form is min søster.

In Danish, a possessive like min, din, hendes, vores, etc. normally replaces the article.

So you say:

• min søster = my sister

not:

• en min søster
• min søsteren

The possessive already makes the noun specific/definite.

Vil gerne is a very common Danish way to express would like to or wants to in a polite, natural way.

• hun vil gerne deltage = she would like to participate / she wants to participate

If you say only vil deltage, it is still grammatical, but it can sound more direct or stronger:

• hun vil deltage = she wants to participate / she intends to participate

So gerne softens the tone and often sounds more natural in everyday Danish.

Because deltage normally goes with the preposition i.

So Danish says:

• deltage i kurset
• deltage i mødet
• deltage i en konkurrence

This is just a verb + preposition pattern you need to learn. It works like English participate in.

Et kursus means a course, while kurset means the course.

The sentence is talking about a specific course, so Danish uses the definite form:

• et kursus = a course
• kurset = the course

So deltage i kurset means participating in the course, not just any course.

Hvis means if and introduces a condition that may or may not be true.

• hvis hun har tid = if she has time

Når means when, and it usually suggests something expected, certain, or repeated.

So here hvis is used because having time is uncertain. She will participate only if she has time.

Danish often uses the present tense to talk about the future, especially in clauses introduced by words like hvis, når, før, and efter.

So:

• hvis hun har tid literally uses present tense
• but it can still mean if she has time later / if she will have time

This is very normal in Danish. Using vil have tid here would usually sound less natural.

Because have time is a fixed idea in both Danish and English.

• har tid = has time / is free

Here tid is used as an uncountable noun, so no article is needed.

If you say en tid, that usually means a time or a period, which is a different meaning.

Om aftenen means something like in the evening or in the evenings, depending on context.

It refers to the evening as a general time period.

• om aftenen = in the evening / in the evenings
• i aften = this evening / tonight

So the sentence is not specifically about tonight. It is talking more generally about whether she has time during the evening.

In a normal Danish main clause, the finite verb usually comes in second position. That is a basic Danish word-order rule.

Here the structure is:

• Min søster = subject
• vil = finite verb
• gerne = adverb
• deltage = infinitive

So:

• Min søster vil gerne deltage ...

This is standard Danish word order. The adverb gerne typically comes after the finite verb and before the infinitive.

Because Danish subordinate clauses do not use the same word order as main clauses.

In the main clause, Danish often has the verb in second position:

• Min søster vil gerne deltage

But after a subordinating conjunction like hvis, the clause usually has:

• conjunction + subject + verb

So:

• hvis hun har tid

not:

• hvis har hun tid

That subject-before-verb order is normal in subordinate clauses.

Because hvis hun har tid om aftenen is a subordinate clause.

Many correct Danish sentences put a comma before a subordinate clause:

• Min søster vil gerne deltage i kurset, hvis hun har tid om aftenen.

You may also see Danish written without that comma, depending on the comma system being used. So the comma here is normal and correct, but you may encounter variation in real texts.