Jeg kan ikke finde svaret på spørgsmålet.

Because this is a main clause in Danish, and Danish normally follows the V2 rule: the finite verb comes in second position.

So the structure is:

• Jeg = subject
• kan = finite verb
• ikke = negation
• finde = infinitive
• svaret på spørgsmålet = object phrase

That is why you get Jeg kan ikke finde ..., not Jeg ikke kan finde ... in a normal main clause.

A useful comparison:

• Jeg kan ikke finde svaret. = main clause
• ... fordi jeg ikke kan finde svaret. = subordinate clause

In a subordinate clause, ikke usually comes before the finite verb.

Because kan is a modal verb, and after a modal verb, the next verb stays in the infinitive.

So:

• kan finde = can find
• not kan finder
• not kan at finde

This is similar to English, where you say can find, not can finds and not can to find.

Here kan means something like can / am able to / manage to.

With ikke, the whole phrase kan ikke finde means:

• cannot find
• am not able to find
• sometimes, depending on context, can’t manage to find

So it is not just about physical ability. It can also mean that the speaker is unable to locate or discover something.

Because both nouns are neuter nouns in Danish:

• et svar = an answer
• et spørgsmål = a question

When a neuter noun becomes definite (the ...), Danish usually adds -et to the end:

• et svar → svaret = the answer
• et spørgsmål → spørgsmålet = the question

So the ending -et is functioning like English the.

Because Danish usually marks definiteness with a suffix attached to the noun, rather than with a separate article.

So instead of:

• the answer
• the question

Danish usually says:

• svaret
• spørgsmålet

This is one of the biggest differences from English.

A separate definite word such as den or det is often used when there is an adjective:

• det rigtige svar = the correct answer
• det svære spørgsmål = the difficult question

But without an adjective, the suffix is the normal choice.

Because Danish uses the fixed pattern svar på noget / svaret på noget for answer to something.

So:

• et svar på et spørgsmål = an answer to a question
• svaret på spørgsmålet = the answer to the question

Even though på often means on, here it is just the normal preposition that goes with svar in this expression. It should be learned as a set phrase:

• svar på
• svaret på

Yes, you could say Jeg kan ikke finde et svar på spørgsmålet, but the meaning changes a little.

• svaret på spørgsmålet = the answer to the question
  This suggests there is one specific answer being looked for.
• et svar på spørgsmålet = an answer to the question
  This sounds less specific and can mean any answer, or at least one possible answer.

So the original sentence points more strongly to a specific, expected answer.

The basic forms are:

• et svar = answer
• et spørgsmål = question

These are the forms you would usually look up in a dictionary.

From those, you build the definite singular forms:

• svaret = the answer
• spørgsmålet = the question

So if you want to learn vocabulary from this sentence, it is best to store the nouns as:

• et svar
• et spørgsmål

That way you remember both the meaning and the gender.

Yes. That is a very important Danish pattern.

In a main clause:

• Jeg kan ikke finde svaret på spørgsmålet.

In a subordinate clause:

• ... fordi jeg ikke kan finde svaret på spørgsmålet.

So in subordinate clauses, ikke normally comes before the finite verb (kan), while in main clauses it comes after the finite verb.

This contrast is one of the most useful word-order patterns for English speakers to learn early.