Åbn den der dåse, hvis du kan, for låget sidder fast.

Åbn is the imperative form of at åbne = to open.

So:

• at åbne = to open
• åbner = open / opens
• åbn! = open!

Danish uses the imperative for direct commands, just like English:

• Åbn døren. = Open the door.
• Åbn den der dåse. = Open that can.

The subject you is not said, but it is understood.

This is a very common way to say that + noun in Danish.

• den = that / the (for common gender nouns)
• der = literally there, but here it helps make a demonstrative meaning
• dåse = can / tin / container

So den der dåse means that can or more literally that can there.

A few useful comparisons:

• en dåse = a can
• dåsen = the can
• den der dåse = that can

This structure is extremely common in spoken Danish.

Because dåse is a common gender noun, not a neuter noun.

In Danish:

• en dåse = a can
• therefore den der dåse = that can

If the noun were neuter, you would use det instead:

• et hus = a house
• det der hus = that house

So the choice between den and det depends on the noun’s grammatical gender.

After a demonstrative like den der, Danish normally uses the noun in its basic singular form, not the suffixed definite form.

So you get:

• den der dåse = that can

not:

• den der dåsen

This is different from English, where the noun does not visibly change anyway. In Danish, it matters.

Compare:

• dåsen = the can
• den der dåse = that can

So even though den can look like the, the whole phrase den der works together as a demonstrative.

It literally means if you can:

• hvis = if
• du = you
• kan = can / are able to

So:

• hvis du kan = if you can

In this sentence, it works like a little inserted comment: if you can.

Yes, the full meaning is something like if you can open it, but Danish often leaves out the second verb when it is obvious from context.

So:

• Åbn den der dåse, hvis du kan
  literally: Open that can, if you can

The missing idea is understood as do it / open it.

English does exactly the same thing:

• Open it, if you can.

So this is very natural in Danish.

Because hvis du kan is inserted as a kind of extra comment in the middle of the sentence.

The main idea is:

• Åbn den der dåse ... for låget sidder fast.

And hvis du kan is added in between as a parenthetical phrase:

• Åbn den der dåse, hvis du kan, for låget sidder fast.

So the commas help show that this part interrupts the main flow for a moment.

Here for means because / since.

So:

• for låget sidder fast = because the lid is stuck

This use of for is a conjunction, not the preposition for.

It is actually quite similar to older or more literary English for meaning because, as in:

• I stayed home, for I was tired.

In modern English that sounds formal or old-fashioned. In Danish, this use is still completely normal, though fordi is also very common.

Because for introduces a new main clause here, and main clauses normally keep regular word order:

• låget = subject
• sidder = verb
• fast = complement/adverb

So:

• for låget sidder fast = because the lid is stuck

This is worth noticing because some Danish sentence connectors affect word order differently, but for here simply links a new clause with normal subject-verb order.

Because the basic noun is:

• et låg = a lid

This is a neuter noun, so the definite singular form ends in -et:

• et låg = a lid
• låget = the lid

So in the sentence:

• låget sidder fast = the lid is stuck

If it were a common gender noun, you would usually expect -en instead.

Sidder fast is a very common Danish expression meaning is stuck, is jammed, or won’t come loose.

Literally, sidder means sits, so the phrase is literally something like sits fast. But in natural English you would normally translate it as:

• is stuck
• is on tight
• won’t budge

Danish often uses sidde for things that are fixed in place, attached, or hard to remove.

Examples:

• Proppen sidder fast. = The cork is stuck.
• Døren sidder fast. = The door is stuck.
• Låget sidder fast. = The lid is stuck.

Yes, dåse is a normal Danish word for a can, tin, or similar container. In Danish, it can refer to a metal container or tin with a lid, so låget is not strange here.

Depending on context, Danish can be more specific:

• konservesdåse = food can / tin can
• øldåse = beer can
• sodavandsdåse = soda can

But plain dåse is a natural general word.

Yes, but it sounds different.

• den der dåse = that can, very common in speech
• denne dåse = this/this particular can, often more formal or written

So in everyday spoken Danish, den der dåse is usually the more natural choice if you are pointing something out.

It has a slightly more conversational feel, while denne can sound more formal, careful, or written.