Nej, jeg kan ikke.

A rough English-friendly pronunciation is:

• Nej ≈ nigh
• jeg ≈ yai (often reduced in everyday speech)
• kan ≈ can
• ikke ≈ IK-uh or EG-uh, depending on accent and how clearly someone speaks

So the whole sentence is roughly:

nigh, yai can IK-uh

Danish pronunciation varies a lot in natural speech, so this is only an approximation, not an exact phonetic guide.

Kan is the present tense of the verb kunne, which means can / be able to.

So:

• jeg kan = I can
• jeg kunne = I could

In this sentence, kan works very much like English can.

Because Danish, like English, can leave the main verb out when it is already understood from the context.

For example:

• Kan du svømme? = Can you swim?
• Nej, jeg kan ikke. = No, I can’t.

The full version could be:

• Nej, jeg kan ikke svømme. = No, I can’t swim.

So jeg kan ikke is a complete and natural reply when the missing action is obvious.

In a normal main clause in Danish, ikke usually comes after the finite verb.

So the standard order is:

• jeg kan ikke

not

• jeg ikke kan in an independent statement

This is a very important Danish word-order pattern.

Compare:

• Jeg kan ikke. = main clause
• ... at jeg ikke kan. = subordinate clause

So in a main clause, kan comes before ikke, but in a subordinate clause, ikke often comes before the verb.

They are not interchangeable.

• nej = no
• ikke = not

So:

• Nej can be used as a full answer by itself.
• ikke is used to negate part of a sentence.

Examples:

• Kan du komme? — Nej.
• Jeg kan ikke komme.

You would not normally say:

• Jeg kan nej.

because nej does not work like not inside a sentence.

In standard Danish, you should normally include the subject:

• Nej, jeg kan ikke.

In casual speech, texting, or very informal dialogue, people may sometimes drop jeg and say something like:

• Kan ikke.

But that is more colloquial and less complete. If you are learning Danish, Nej, jeg kan ikke is the safe and correct version to use.

The comma separates the introductory response word Nej from the full clause jeg kan ikke.

So:

• Nej, jeg kan ikke.

is a very normal written form.

It works much like English:

• No, I can’t.

In very casual writing, people may leave the comma out, but using it is standard and clear.

Yes. Kan can express several related ideas, depending on context, just like English can.

It can mean:

• ability: Jeg kan svømme = I can swim
• possibility: Det kan ske = That can happen
• permission: Du kan gå nu = You can go now

In Nej, jeg kan ikke, the exact nuance depends on the situation. It might mean:

• I’m not able to
• I’m not allowed to
• I can’t do that
• I can’t come

The missing context tells you which one is meant.

In a question, the verb usually comes before the subject:

• Kan jeg ikke? = Can’t I?

In a subordinate clause, ikke usually comes before the verb:

• Han siger, at jeg ikke kan. = He says that I can’t.

So compare these patterns:

• Jeg kan ikke. = main clause
• Kan jeg ikke? = question
• ... at jeg ikke kan. = subordinate clause

This is one of the key word-order patterns in Danish grammar.