Hvis jeg ikke kan finde min nøgle, leder jeg efter den i tasken.

Because hvis introduces a subordinate clause. In Danish, words like ikke, altid, ofte, and other sentence adverbs usually come before the finite verb in subordinate clauses.

Compare:

• Jeg kan ikke finde min nøgle. = main clause
• Hvis jeg ikke kan finde min nøgle ... = subordinate clause

So this is normal Danish word order, not a special exception.

This is because Danish main clauses follow the verb-second rule.

The whole Hvis jeg ikke kan finde min nøgle counts as the first element in the sentence. That means the finite verb of the main clause must come next, in second position:

• Hvis jeg ikke kan finde min nøgle, leder jeg efter den i tasken.

If the main clause stood alone, it would be:

• Jeg leder efter den i tasken.

So the word order changes because the if-clause comes first.

Kan finde means can find or am able to find. In this sentence, it gives the idea of being unable to locate the key.

• Hvis jeg ikke kan finde min nøgle ... = If I can’t find my key ...
• Hvis jeg ikke finder min nøgle ... = If I don’t find my key ...

Both are possible in some contexts, but they are slightly different:

• ikke kan finde focuses on inability at that moment
• ikke finder focuses more on the result

So ikke kan finde is very natural here.

They describe two different stages:

• finde = to find
• lede efter = to look for / search for

So the sentence means:

• first: I cannot find the key
• then: I look for it in the bag

That is why both expressions appear in the same sentence.

Because lede efter works as a verb + preposition combination, similar to English look for.

You say:

• lede efter noget = look for something
• leder efter den = look for it

The object belongs after the preposition efter, not before it.

So:

• correct: leder efter den
• not natural: leder den efter

In Danish, when you use a possessive like min, din, hans, hendes, etc., the noun usually stays in its basic indefinite form.

So:

• min nøgle = my key
• din taske = your bag
• hans bil = his car

You normally do not add the definite ending at the same time. So min nøglen would be wrong.

Because nøgle is a common-gender noun, an en-word:

• en nøgle = a key

For singular common-gender nouns, Danish uses den as the pronoun:

• min nøgle → den

If the noun were a neuter noun, an et-word, the pronoun would usually be det instead.

Tasken means the bag. The ending -en is the normal Danish way of making many common-gender nouns definite.

• en taske = a bag
• tasken = the bag

Here the bag is understood as a specific one, probably a bag already known from the situation, such as my bag or the bag I usually keep it in.

I tasken means in the bag / inside the bag.

• i is used for being inside something
• på usually means on top of something, or on some surfaces

So if the key might be inside the bag, i tasken is the natural choice.

Sometimes, but the meaning changes a bit.

• hvis = if
• når = when / whenever

So:

• Hvis jeg ikke kan finde min nøgle ... = If I can’t find my key ...
• Når jeg ikke kan finde min nøgle ... = When(ever) I can’t find my key ...

Hvis presents it as a condition.
Når makes it sound more like something that actually happens from time to time.

Both can be possible depending on context, but hvis is the more direct match for English if.

Because Danish often uses the present tense for general situations, habits, or normal reactions.

So this sentence can mean something like:

• Whenever this situation happens, this is what I do.

That is why present tense works well here:

• kan finde
• leder

If you wanted to make it sound more like a specific future action, you could say something like vil jeg lede efter den, but the original sentence is perfectly natural for a general statement.