Hendes penalhus er lille, men der er både en lommeregner og to blyanter i det.

Penalhus means pencil case.

It is a neuter noun in Danish, so its basic form is:

• et penalhus = a pencil case
• penalhuset = the pencil case

That neuter gender matters later in the sentence, because it affects the pronoun det.

This is a very common question.

Danish uses sin / sit / sine only when the owner is also the subject of the same clause.

Here, in Hendes penalhus er lille, the subject is penalhus, not the woman/girl who owns it. So Danish uses hendes.

Compare:

• Hun har sit penalhus. = She has her own pencil case.
  Here hun is the subject, so sit is possible.

• Hendes penalhus er lille. = Her pencil case is small.
  Here the subject is penalhus, so you use hendes.

So hendes is correct because the possessor is not the grammatical subject of the clause.

Because lille is irregular.

Many Danish adjectives add -t in the neuter singular:

• en stor taske
• et stort hus

But lille does not work that way. It stays lille in the singular, including with neuter nouns:

• en lille bog
• et lille penalhus

So penalhus is neuter, but the correct form is still lille.

Der er is the normal Danish way to say there is or there are.

So:

• der er en lommeregner = there is a calculator
• der er to blyanter = there are two pencils

In this kind of sentence, der does not mean there as a place. It is just part of the existential structure der er.

A useful thing to remember: Danish uses er in both singular and plural here:

• der er en bog
• der er to bøger

English changes between there is and there are, but Danish usually just keeps der er.

Både ... og means both ... and.

In this sentence:

• både en lommeregner og to blyanter

means:

• both a calculator and two pencils

It is used to connect two things and emphasize that both are present.

This is a very common pattern in Danish:

• Hun taler både dansk og engelsk.
• Vi købte både brød og mælk.

Because Danish uses an indefinite article with singular countable nouns, but not with plural nouns after a number.

So:

• en lommeregner = a calculator
• to blyanter = two pencils

This is similar to English:

• a calculator
• two pencils

You would not say to en blyanter, just like you would not say two a pencils in English.

I det means in it.

The preposition i means in, and det is the pronoun it referring back to penalhus.

So:

• i det = in it

Danish often uses a pronoun like this instead of repeating the noun:

• Hun har et penalhus. Der er to blyanter i det.

That sounds more natural than repeating penalhuset again and again.

Because penalhus is a neuter noun: et penalhus.

In Danish, pronouns often match grammatical gender:

• nouns with en often take den
• nouns with et often take det

So:

• en bog → den
• et penalhus → det

That is why the sentence ends with i det.

Because men means but, and in standard Danish writing it is normally preceded by a comma when it links two clauses.

So the structure is:

• Hendes penalhus er lille,
• men der er både en lommeregner og to blyanter i det.

This is normal Danish punctuation.

Yes, it could. For example:

• Hendes penalhus er lille, men der er både en lommeregner og to blyanter i penalhuset.

That is grammatically fine, but it sounds heavier and less natural in ordinary speech and writing. Once penalhus has already been mentioned, Danish usually prefers the pronoun det.

So i det is the more natural choice here.