Jeg kan ikke skrive ordet rigtigt uden ordbogen.

Because in a normal Danish main clause, the finite verb usually comes in second position. That is the famous V2 word order.

• Jeg = subject
• kan = finite verb
• ikke = negation

So the natural order is:

Jeg kan ikke skrive ...

If this were a subordinate clause, the word order would change:

... at jeg ikke kan skrive ordet rigtigt ...

So English speakers often need to learn that Danish word order changes depending on whether the clause is main or subordinate.

Kan is the present tense of kunne, meaning can / am able to.

After modal verbs such as kan, vil, skal, må, burde, Danish normally uses the infinitive without at:

• Jeg kan skrive
• not Jeg kan at skrive

So kan skrive works like English can write.

In Danish, skrive et ord rigtigt can mean write/spell a word correctly. So skrive is often used where English specifically says spell.

Danish also has the verb stave, which means to spell. So you could also say:

Jeg kan ikke stave ordet rigtigt uden ordbogen.

That version makes the spelling idea more explicit. But skrive ordet rigtigt is still natural Danish.

The basic noun is ord = word.

It is a neuter noun, so its indefinite singular form is:

• et ord = a word

The definite singular form is made by adding the article to the end:

• ordet = the word

So:

• et ord = a word
• ordet = the word

This is very common in Danish: the definite article is usually a suffix, not a separate word.

Here rigtigt is being used adverbially, meaning correctly.

A very common pattern in Danish is that an adjective gets -t when used as an adverb:

• Han skriver rigtigt. = He writes correctly.
• Det er rigtigt. = That is correct.

So in this sentence, rigtigt describes how the word is written/spelled.

It is not describing the noun ordet directly. It is describing the action skrive.

Here it means correctly.

That is because it goes with skrive ordet:

skrive ordet rigtigt = write/spell the word correctly

You may also see rigtigt used in colloquial Danish to mean really or very, for example:

• Det er rigtigt godt. = It is really good.

But that is not the meaning here.

Because Danish usually writes compound nouns as a single word.

So:

• ord = word
• bog = book
• ordbog = dictionary

English often separates things more, but Danish strongly prefers one written compound. This is an important pattern to get used to.

Then the definite form becomes:

• ordbogen = the dictionary

Because ordbog is a common gender noun.

Its forms are:

• en ordbog = a dictionary
• ordbogen = the dictionary

So the definite singular ending for this noun is -en.

Compare:

• en bog → bogen
• en stol → stolen

This is different from ord, which is neuter:

• et ord → ordet

So the sentence contains both common gender and neuter nouns:

• ordet from et ord
• ordbogen from en ordbog

All three are possible, but they mean slightly different things.

• uden ordbogen = without the dictionary
  This suggests a specific dictionary already known in the context.

• uden en ordbog = without a dictionary
  This means without any dictionary, in a more countable, specific sense.

• uden ordbog = without dictionary / without using a dictionary
  This can sound more general or idiomatic.

So the sentence you were given points to a particular dictionary: ordbogen.

Because the natural Danish order here is:

verb + object + adverb

So:

• skrive ordet rigtigt

is normal, while:

• skrive rigtigt ordet

sounds wrong in standard Danish.

The object ordet comes right after the verb, and rigtigt follows as an adverb describing the action.

Yes, absolutely.

That version is very natural and may even feel more directly equivalent to English I can’t spell the word correctly without the dictionary.

A useful distinction is:

• skrive ordet rigtigt = write/spell the word correctly
• stave ordet = spell the word

If you want to emphasize spelling, stave is a very good choice.

Yes. Rigtigt is a word many learners find hard to pronounce.

In careful speech, it is roughly something like:

RIG-tit or RI-ti(t)

But actual pronunciation varies, and the middle consonants are often softened or reduced in everyday speech.

The important thing for learners is:

• do not pronounce every letter very strongly
• the g is not a hard English g
• the word is often more reduced than its spelling suggests

So this is a good word to learn by listening, not just by reading.