Fejebakken ligger bag døren, så jeg kan samle glasskårene op.

Danish often uses position verbs where English would simply use to be.

• ligger = lies / is lying / is located in a lying position
• står = stands / is standing
• sidder = sits / is sitting

So Fejebakken ligger bag døren is more natural Danish than just Fejebakken er bag døren.

A Danish speaker often chooses the verb based on how something is positioned:

• Bogen ligger på bordet = The book is on the table
• Flasken står på bordet = The bottle is on the table
• Barnet sidder på stolen = The child is on the chair

With a dustpan, ligger sounds natural because it is thought of as lying there.

In Danish, the definite article is usually attached to the end of the noun.

• en fejebakke = a dustpan

• fejebakken = the dustpan

• en dør = a door
• døren = the door

So the endings work like English the.

The most common definite endings are:

• -en for many common gender nouns
• -et for many neuter nouns

If there is an adjective before the noun, Danish often uses a separate definite word too:

• døren = the door
• den røde dør = the red door

Here, så is best understood as so that.

So:

• Fejebakken ligger bag døren, så jeg kan samle glasskårene op = The dustpan is behind the door, so that I can pick up the shards of glass

In natural English, you might simply say so I can..., but in Danish the structure here points to the meaning so that I can...

This is different from another very common så, which means so / then / therefore in a main clause.

Because this så introduces a subordinate clause.

In a subordinate clause, Danish normally keeps the order:

• subject + verb
• jeg kan

So:

• så jeg kan samle glasskårene op = so that I can pick up the shards of glass

If you said:

• så kan jeg samle glasskårene op

that would be a main clause after så, meaning more like:

• so/then I can pick up the shards of glass

So the two patterns are different:

• så jeg kan ... = so that I can ...
• så kan jeg ... = so / then I can ...

This is a very important Danish word-order difference.

Because after a modal verb, Danish uses the bare infinitive without at.

So you say:

• jeg kan samle = I can pick up
• jeg vil samle = I want to pick up
• jeg skal samle = I have to pick up

Not:

• jeg kan at samle ❌

This is similar to English:

• I can go
• not I can to go

By contrast, some other verbs do take at:

• jeg prøver at samle glasskårene op = I am trying to pick up the shards of glass

Because samle op is a verb + particle combination, similar to English pick up.

The basic meaning is:

• samle = gather / collect
• samle op = pick up

In Danish, the particle often gets separated and placed later in the clause:

• Jeg samler glasskårene op
• Jeg kan samle glasskårene op

This is very common in Danish, just like in English:

• pick the glass up
• pick up the glass

So samle ... op works as one meaning, even though the words are separated.

Glasskårene is the definite plural form of glasskår, which means shards/pieces of broken glass.

It breaks down like this:

• glas = glass
• skår = shard / chip / broken piece
• glasskår = shard of glass / broken glass piece
• glasskårene = the shards of glass

A useful mini-paradigm:

• et glasskår = a shard of glass
• glasskår = shards of glass
• glasskårene = the shards of glass

So the ending -ene here marks definite plural.

Because Danish uses compound nouns very often, and they are normally written as one word.

Examples in this sentence:

• fejebakke = feje
  • bakke
• glasskår = glas
  • skår

This is extremely common in Danish. English sometimes writes similar ideas as separate words, but Danish usually joins them.

Compare:

• en tandbørste = a toothbrush
• et spisebord = a dining table
• et vindueglas = a windowpane / window glass

For English speakers, this is something to watch carefully: what would be two words in English is often one word in Danish.

Yes. If you want a more straightforward result meaning, you could say:

• Fejebakken ligger bag døren, så kan jeg samle glasskårene op.

That means more like:

• The dustpan is behind the door, so/then I can pick up the shards of glass.

The original sentence:

• ... så jeg kan samle glasskårene op

sounds more like so that I can..., expressing purpose or intended result.

So both are possible ideas, but the word order changes the meaning.

Yes. Bag is the preposition behind.

So:

• bag døren = behind the door

This is a normal prepositional phrase:

• bag huset = behind the house
• bag bilen = behind the car

In the sentence, døren is definite because it refers to a specific door known from the situation, not just any door.