Jeg tager mit festtøj på senere, men min søster siger, at hendes festtøj stadig hænger i skabet.

Because tage ... på is a separable verb phrase meaning to put on.

In a main clause, Danish normally puts the finite verb in second position, so tager comes early and the particle på stays later:

• at tage festtøj på = to put on party clothes
• Jeg tager mit festtøj på senere = I’m putting on my party clothes later

This happens with many Danish verb-particle combinations, such as stå op, gå ud, and tage af.

Because Danish possessives must agree with the noun they go with.

• min is used with common gender singular nouns
• mit is used with neuter singular nouns

So:

• min søster because søster is a common-gender noun
• mit festtøj because festtøj is a neuter noun

A useful pattern is:

• min bil
• mit hus
• mine venner

Grammatically, it is singular and usually treated as an uncountable noun, like clothing in English.

So even though English often says clothes, Danish uses tøj as a singular mass noun:

• tøj = clothes / clothing
• festtøj = party clothes / party outfit / dress clothes

That is why the sentence uses mit, not a plural form.

Danish often uses the present tense for future meaning when the time is clear from context.

Here, senere shows that the action will happen in the future:

• Jeg tager mit festtøj på senere = I’ll put on my party clothes later

This is very normal in Danish. English does something similar in sentences like I’m leaving tomorrow.

At introduces a subordinate clause and usually corresponds to English that.

So:

• min søster siger, at ... = my sister says that ...

In English, that is often left out, but in Danish at is commonly kept, especially in writing.

Because the part after at is a subordinate clause, and Danish word order changes in subordinate clauses.

In a subordinate clause, words like stadig, ikke, nok, and aldrig usually come before the finite verb.

So:

• at hendes festtøj stadig hænger i skabet

Compare that with a main clause:

• Hendes festtøj hænger stadig i skabet

This is a very important Danish word-order pattern.

This is about reflexive possessives.

Danish uses sin / sit / sine when the possessor is the subject of the same clause and the possessive is not part of the subject itself.

But here the possessive is inside the subject of the subordinate clause:

• hendes festtøj stadig hænger i skabet

So hendes is used, not sit.

A clear comparison:

• Hun hænger sit festtøj i skabet = She hangs her own party clothes in the closet
  
  • Here sit refers back to the subject hun

But in your sentence, the structure is different, so hendes is the natural choice.

Because skabet is the definite form, meaning the closet / the wardrobe / the cupboard.

Danish usually adds the definite article to the end of the noun:

• et skab = a closet / a cupboard
• skabet = the closet / the cupboard

So i skabet means in the closet/wardrobe, referring to a specific one.

Because Danish often describes where something is by using a verb that matches its physical position.

For clothes on a hanger, hænge is very natural:

• hænger = hangs / is hanging

So festtøjet stadig hænger i skabet means the clothes are still hanging there in the closet.

This is part of a broader Danish pattern:

• stå for things that stand
• ligge for things that lie
• hænge for things that hang

Skab is a broad Danish word for a storage unit, so the exact English translation depends on context.

It can mean things like:

• cupboard
• cabinet
• closet
• wardrobe

Because this sentence is about clothes, i skabet most naturally means in the closet or in the wardrobe.