Ne mogu riješiti ovu zagonetku.

In Croatian, the negative particle ne is usually written separately from the verb:

• mogu = I can
• ne mogu = I cannot / I can’t

So ne mogu riješiti ovu zagonetku literally breaks down as:

• ne = not
• mogu = I can
• riješiti = solve
• ovu zagonetku = this puzzle/riddle

A few Croatian verbs do have special negative forms written together, but moći is not one of them, so ne mogu is correct.

Mogu is the 1st person singular present tense of the verb moći (to be able, can).

So:

• ja mogu = I can
• ti možeš = you can
• on/ona/ono može = he/she/it can
• mi možemo = we can
• vi možete = you can
• oni/one/ona mogu = they can

In this sentence, mogu tells you the subject is I, even though ja is not stated.

Croatian often leaves out subject pronouns when they are already clear from the verb ending.

So instead of saying:

• Ja ne mogu riješiti ovu zagonetku.

Croatian very naturally says:

• Ne mogu riješiti ovu zagonetku.

Because mogu already means I can, the I is understood.

You can include ja if you want extra emphasis, for example:

• Ja ne mogu riješiti ovu zagonetku. = I can’t solve this puzzle.
  (possibly contrasting with someone else who can)

Because after the modal verb moći (can / be able to), Croatian normally uses the infinitive.

So the pattern is:

• mogu + infinitive = can + verb
• ne mogu + infinitive = cannot + verb

Examples:

• Mogu doći. = I can come.
• Ne mogu spavati. = I can’t sleep.
• Ne mogu riješiti ovu zagonetku. = I can’t solve this puzzle.

This is similar to English can solve, although English uses the bare verb form and Croatian uses the infinitive.

Riješiti is the perfective verb, meaning to solve something successfully / to completion.

In this sentence, that makes sense because the speaker means they cannot bring the action to a finished result:

• Ne mogu riješiti ovu zagonetku. = I can’t solve this puzzle.
  (I can’t get it solved.)

Croatian often distinguishes between:

• perfective verbs: completed whole actions
• imperfective verbs: ongoing, repeated, habitual, or process-focused actions

For a single puzzle or riddle, riješiti is the natural choice because the goal is a completed result.

Because zagonetku is the direct object of the verb riješiti, so it must be in the accusative case.

The basic dictionary form is:

• zagonetka = puzzle, riddle
  (nominative singular)

But after a verb like riješiti (to solve), you need the object form:

• zagonetku = puzzle/riddle
  (accusative singular)

The demonstrative this also changes to match the noun:

• ova zagonetka = this puzzle/riddle
  (nominative)
• ovu zagonetku = this puzzle/riddle
  (accusative)

So both words change because Croatian adjectives/demonstratives agree with the noun in:

• gender
• number
• case

They match each other grammatically.

• zagonetka is feminine singular
• In this sentence it is in the accusative singular
• So the demonstrative this must also be feminine singular accusative

That gives:

• ovu zagonetku

This kind of agreement is very important in Croatian. The same thing happens with adjectives:

• tešku zagonetku = a difficult puzzle
• ovu tešku zagonetku = this difficult puzzle

All the words describing the noun have to match it.

Yes. Croatian word order is more flexible than English word order because cases show the grammatical roles.

The neutral order here is:

• Ne mogu riješiti ovu zagonetku.

But you could also say:

• Ovu zagonetku ne mogu riješiti.

This puts more focus on this puzzle.

You might also hear:

• Ne mogu ovu zagonetku riješiti.

That is also possible, though the first version is usually the most neutral and common for learners to start with.

So the meaning stays basically the same, but the emphasis can change.

Yes, many speakers would understand and use that structure, especially in some regional varieties and in everyday speech across the wider South Slavic area.

That version uses:

• ne mogu da riješim instead of
• ne mogu riješiti

In standard Croatian, the modal + infinitive pattern is generally the safest and most standard choice:

• Ne mogu riješiti ovu zagonetku.

So if you are learning standard Croatian, this is the form to prefer.

Zagonetka often means riddle, but it can also mean puzzle depending on context.

So the sentence could be understood as:

• I can’t solve this riddle.
• I can’t solve this puzzle.

If the context is a word puzzle, mystery, or brain teaser, zagonetka works well. The exact English translation depends on what kind of thing is being solved.

A rough pronunciation guide:

• riješiti ≈ ree-yeh-shee-tee
• zagonetku ≈ za-go-NET-koo

A few helpful points:

• š sounds like sh in shoe
• j sounds like English y in yes
• r is rolled or tapped
• Croatian spelling is quite regular, so words are usually pronounced as written

So:

• riješiti: the j gives a y sound, not an English j
• zagonetku: the stress is often heard around -net-, though Croatian stress is not usually marked in normal writing

Yes, it is completely natural and idiomatic.

Ne mogu riješiti ovu zagonetku. is a very normal way to say:

• I can’t solve this puzzle.
• I can’t solve this riddle.

It sounds like standard, everyday Croatian and is a good model sentence for learning:

• negation with ne
• the modal verb moći
• infinitive after a modal
• accusative object
• demonstrative-noun agreement