Kan du give mig værktøjet, så jeg kan gøre stolen færdig?

Because this is a question.

In Danish, a yes/no question usually starts with the verb first, then the subject:

• Kan du ...? = Can you ...?
• Har du ...? = Have you ...?
• Vil du ...? = Will you / would you ...?

If you say Du kan ..., that is normally a statement, not a question:

• Du kan give mig værktøjet. = You can give me the tool.

So Kan du give mig værktøjet ...? is the normal question pattern.

Kan du ...? is a very common and natural way to ask for something in Danish. It is not automatically rude.

It often works like English Can you ...?

• Kan du hjælpe mig? = Can you help me?
• Kan du give mig værktøjet? = Can you give me the tool?

If you want to sound a bit softer or more polite, Danish can also use:

• Vil du ...? = often like Would you ...?
• Kunne du ...? = Could you ...?

For example:

• Kunne du give mig værktøjet?
• Vil du give mig værktøjet?

But Kan du is completely normal in everyday speech.

Because give normally takes an indirect object directly in Danish, just like in English give me.

So:

• give mig = give me
• give ham = give him
• give os = give us

You usually do not say give til mig here.

Compare:

• Kan du give mig værktøjet? = Can you give me the tool?

This is the normal pattern:

• give + person + thing

So:

• give mig værktøjet
• literally: give me the tool

Because værktøjet is the definite form, meaning the tool.

In Danish, many nouns add the definite article to the end of the word instead of using a separate word like English the.

• et værktøj = a tool
• værktøjet = the tool

This noun is a neuter noun because it takes et in the indefinite form.

A common pattern is:

• et
  • noun = indefinite singular
• noun + -et = definite singular

So:

• et værktøj → værktøjet

For the same reason: stolen is the definite form, meaning the chair.

• en stol = a chair
• stolen = the chair

This noun is a common gender noun because it takes en in the indefinite form.

Typical pattern:

• en stol = a chair
• stolen = the chair

So in the sentence:

• gøre stolen færdig = finish the chair

Here så means so that or so in the sense of for that purpose.

The sentence is structured like this:

• Kan du give mig værktøjet = Can you give me the tool
• så jeg kan gøre stolen færdig = so that I can finish the chair

So så introduces the reason/purpose/result clause.

It is very common in Danish to use så this way:

• Skynd dig, så vi kan nå toget. = Hurry up so that we can catch the train.

In everyday English, you might translate it simply as so:

• Can you give me the tool so I can finish the chair?

Because the second part is a new clause with its own verb.

The sentence has two parts:

1. Kan du give mig værktøjet
2. så jeg kan gøre stolen færdig

In the second clause, jeg is the subject, and kan is the modal verb meaning can / am able to.

So:

• jeg kan gøre stolen færdig = I can finish the chair

Even though English also repeats can here, learners sometimes expect Danish to leave it out. But Danish needs it because this is a full clause.

Gøre færdig is a common Danish expression meaning to finish, to complete, or to get something done.

Literally, gøre means do/make, and færdig means finished/ready, but together they function like:

• finish
• complete

Examples:

• gøre arbejdet færdigt = finish the work
• gøre stolen færdig = finish the chair

This is one of those Danish expressions where the meaning is best learned as a unit.

Also notice that færdig can appear after the object:

• gøre stolen færdig

That word order is normal.

Because in gøre stolen færdig, færdig describes stolen, and stol is a common gender noun:

• en stol
• therefore: færdig

Compare:

• gøre stolen færdig = finish the chair
• gøre bordet færdigt = finish the table

Why the difference?

• en stol → færdig
• et bord → færdigt

So the ending agrees with the noun being described.

Yes, in this kind of everyday situation, gøre stolen færdig sounds much more natural.

Afslutte often means conclude, end, or finish in a more abstract or formal sense, such as:

• afslutte et møde = end a meeting
• afslutte et projekt = complete a project

For physically finishing work on an object, Danish very often uses:

• gøre ... færdig

So for a chair someone is working on, gøre stolen færdig is very natural.

Because after så, the clause here is functioning as a subordinate clause, and Danish subordinate clauses usually keep the subject before certain sentence adverbs and follow normal clause order with the subject visible early.

So:

• så jeg kan gøre stolen færdig

is the normal pattern.

If you said så kan jeg ..., that would sound more like a main clause meaning something like:

• and then I can ...
• so I can ...

In this sentence, the meaning is specifically so that I can ..., which fits så jeg kan ... very well.

Yes, possibly, depending on the situation.

• give mig værktøjet = give me the tool
• række mig værktøjet = hand me the tool / pass me the tool

If the tool is nearby and you want someone to pass it to you, række mig værktøjet may sound even more precise.

If you want a general request, give mig værktøjet is fine and easy to understand.

So both can work, but:

• give = broader, more general
• række = specifically pass/hand over

The given sentence is already natural, but in everyday speech a Dane might also say:

• Kan du give mig værktøjet, så jeg kan få stolen færdig?
• Kan du række mig værktøjet, så jeg kan gøre stolen færdig?

The original sentence is completely good Danish. In speech, the main difference is often just choice of verb:

• give
• række
• sometimes få ... færdig instead of gøre ... færdig

But Kan du give mig værktøjet, så jeg kan gøre stolen færdig? is absolutely normal and understandable.