Hendes postkasse er fuld, fordi naboerne sender mange kort med flotte frimærker.

Hendes means her.

Danish distinguishes between:

• hendes / hans / deres = her / his / their
• sin / sit / sine = reflexive possessive, meaning his/her/its/their own, when it refers back to the subject of the clause

Compare:

• Hun tømmer sin postkasse = She empties her own mailbox.
• Hun tømmer hendes postkasse = She empties another woman’s mailbox.

In Hendes postkasse er fuld, hendes simply tells you whose mailbox it is: her mailbox.

Because Danish forms compound nouns very freely, much like German.

So:

• post = mail/post
• kasse = box

Together, postkasse means mailbox.

This is very normal in Danish. English often writes these as one word, two words, or with a hyphen depending on the expression, but Danish usually prefers one solid compound word.

Other examples:

• sommerhus = summer house
• togstation = train station
• frimærkesamling = stamp collection

Because adjectives in Danish change form depending on gender and number.

Here, postkasse is a common gender singular noun: en postkasse.
So the adjective stays in its basic form: fuld.

Compare:

• Postkassen er fuld = The mailbox is full.
• Brevet er fuldt = The letter is full.
• Postkasserne er fulde = The mailboxes are full.

So in this sentence, fuld matches a singular common gender noun.

Because -ne marks the definite plural.

The noun is:

• en nabo = a neighbor
• naboer = neighbors
• naboerne = the neighbors

So naboerne is not just any neighbors; it refers to a specific group, the neighbors.

This is a very common Danish pattern:

• biler = cars
• bilerne = the cars

Because fordi introduces a subordinate clause, and subordinate clauses normally use subject + verb order in standard Danish.

So:

• Hendes postkasse er fuld = main clause
• fordi naboerne sender mange kort med flotte frimærker = subordinate clause

After fordi, you usually get:

• subject: naboerne
• verb: sender

This is different from main-clause Danish, where the verb often comes in second position.

A useful comparison:

• Naboerne sender mange kort. = main clause
• ... fordi naboerne sender mange kort. = subordinate clause

Sender is the present tense of at sende = to send.

So:

• at sende = to send
• sender = send / sends / are sending

Like many languages, Danish present tense can cover both:

• a habitual action: The neighbors send many cards
• an action happening around now: The neighbors are sending many cards

In this sentence, the most natural reading is probably habitual or repeated action.

Because mange is used with countable plural nouns, while meget is used with uncountable nouns or amount words.

So:

• mange kort = many cards
• meget post = much mail
• meget vand = much water

Since kort is a countable thing and it is plural here, mange is the correct choice.

Here, kort is plural, because it follows mange.

The reason it may look confusing is that some Danish nouns have the same form in singular and plural indefinite.

For kort:

• et kort = a card
• kort = cards
• kortet = the card
• kortene = the cards

So the form kort can mean either card or cards, and the context tells you which one it is.
In mange kort, it must be plural.

Yes, most naturally med flotte frimærker describes kort.

So the idea is:

• mange kort med flotte frimærker = many cards with beautiful stamps

In other words, the neighbors are sending cards that have nice stamps on them.

The preposition med usually means with, and here it adds extra information about the cards.

Because frimærker is plural, and adjectives before plural nouns usually take -e.

So:

• et flot frimærke = a beautiful stamp
• flotte frimærker = beautiful stamps

This -e ending is very common with plural nouns.

You will also see -e with definite forms:

• de flotte frimærker = the beautiful stamps

Because Danish usually does not use an article with indefinite plural nouns in expressions like this.

So:

• mange kort = many cards
• flotte frimærker = beautiful stamps

That is normal Danish grammar.

If the noun were definite, you would see a definite article word:

• de flotte frimærker = the beautiful stamps

So in the sentence, the cards and stamps are presented as indefinite, not as a specific already-known set.