Den lange forklaringen kan forvirre barna.

Two things are happening:

1. Definite noun

   • forklaring = an explanation (indefinite)
   • forklaringen = the explanation (definite, with the ending -en)

2. Adjective agreement in the definite form
   In Norwegian, when an adjective comes before a definite noun, the adjective gets an extra -e, and you also add den / det / de in front:

   • en lang forklaring = a long explanation
   • den lange forklaringen = the long explanation

So you need:

• den (definite article in front)
• lange (adjective in definite form)
• forklaringen (noun in definite form)

den lang forklaring is incorrect because:

• lang should be lange before a definite noun
• forklaring should be forklaringen when you mean the explanation

Forklaring is grammatically feminine in origin, but in Bokmål it is usually treated as common gender (masculine).

So you’ll see:

• en forklaring – an explanation
• forklaringen – the explanation

You can use the feminine forms in some styles of Bokmål:

• ei forklaring – an explanation
• forklaringa – the explanation

In the sentence Den lange forklaringen kan forvirre barna, the writer is using the more neutral/common style:
en forklaring → forklaringen (with -en).

Yes, this is the well-known “double definiteness” pattern in Norwegian (and Swedish):

• With no adjective:

  • forklaringen = the explanation (only the suffix shows definiteness)

• With an adjective in front:
  You must use both:

  • den lange forklaringen = the long explanation

So the rule in Bokmål main patterns:

• Definite noun alone: forklaringen
• Definite noun + adjective: den + adjective-e + noun-en
  
  • den lange forklaringen
  • det store huset (the big house)
  • de små barna (the small children)

Leaving out either den or the -en in this structure is wrong in standard Bokmål.

• forklaring = an explanation / explanation in general (indefinite)

  • Jeg trenger en forklaring. = I need an explanation.

• forklaringen = the explanation (definite, specific)

  • Den lange forklaringen kan forvirre barna. = The long explanation can confuse the children.

In your sentence, we are talking about one specific explanation that is already known in the context, so the definite form forklaringen is used.

Barn is an irregular neuter noun:

• et barn = a child
• barnet = the child
• barn = children (indefinite plural)
• barna = the children (definite plural)

So the forms are:

• singular indefinite: et barn
• singular definite: barnet
• plural indefinite: barn
• plural definite: barna

There is no form barnene or barner in standard Norwegian. In the sentence, we mean the children, so barna is correct.

The -a at the end of barna already marks it as definite plural: the children.

• barn = children
• barna = the children

If you add de, you change the meaning slightly:

• barna = the children (in general / the group already known)
• de barna = those children / those particular children

So Den lange forklaringen kan forvirre barna =
The long explanation can confuse the children (in general / the ones we’re talking about).

De barna would focus more on a specific subset: those children.

The word order is standard S–V–O (Subject – Verb – Object):

• Subject: Den lange forklaringen (the long explanation)
• Verb (modal): kan (can)
• Verb (main, infinitive): forvirre (confuse)
• Object: barna (the children)

So structurally:

[Den lange forklaringen] [kan] [forvirre] [barna].

This is a normal main-clause word order in Norwegian when nothing is moved to the front except the subject.

In Norwegian, modal verbs are followed by the bare infinitive, without å:

Common modals:

• kan – can
• vil – will / want to
• må – must / have to
• skal – shall / going to
• bør – should
• får (in the sense is allowed to)

Pattern:

• kan forvirre – can confuse
• vil hjelpe – wants to help / will help
• må gå – must go

So kan å forvirre is ungrammatical; you must say kan forvirre.

Norwegian uses this pattern:

• A modal verb (kan) is conjugated: kan (present tense of å kunne)
• The main verb comes after it in the infinitive, without å

So:

• kan forvirre – can confuse
• kan se – can see
• kan lese – can read

If you had no modal, you would conjugate forvirre:

• Den lange forklaringen forvirrer barna.
  = The long explanation confuses the children.

With kan, you must use the infinitive: kan forvirre.

Kan is the present tense of the modal verb å kunne (to be able to / can).

• Den lange forklaringen forvirrer barna.
  = The long explanation confuses the children (it actually does; statement of fact, or habit).

• Den lange forklaringen kan forvirre barna.
  = The long explanation can confuse the children (it has the potential to do so, it may happen).

So kan emphasizes possibility or capability, not that it always happens.

Yes, that is a natural alternative with a slightly different structure:

• Den lange forklaringen kan forvirre barna.
  – The long explanation can confuse the children.
  (Focus on the effect it has on them, as an action.)

• Den lange forklaringen kan være forvirrende for barna.
  – The long explanation can be confusing for the children.
  (Focus on the property of the explanation: it is confusing.)

Both are correct and close in meaning, but the original sentence is more directly verb–object (confuse the children).

• lang forklaring = a long explanation / long explanation (indefinite)

  • Det var en lang forklaring. = It was a long explanation.

• den lange forklaringen = the long explanation (definite, specific one)

  • Den lange forklaringen kan forvirre barna.

So:

• No den, no -en → indefinite (a / some)
• With den + -en → definite (the).

Approximate IPA and an English-friendly hint:

• den – /den/ (like den in Denmark, short e)

• lange – /ˈlɑŋə/

  • la like la in lava but shorter
  • ng like ng in singer
  • final e is a short, unstressed uh sound

• forklaringen – /fɔrˈklɑːrɪŋən/ (Bokmål-style)

  • for like English for but often with a short o
  • stress on kla: klaa (long a)
  • r is tapped or trilled, depending on dialect
  • final -en is again a short, weak ən

• kan – /kɑn/

  • like kun in kung fu but with a as in father (short)

• forvirre – /fɔrˈvɪrːə/

  • stress on vir
  • rr is usually a long tapped or trilled r
  • final e weak uh

• barna – /ˈbɑːrnɑ/ (east/north) or /ˈbɑːɳɑ/ (retroflex rn in many dialects)

  • ba with long a as in father
  • rn often merges into a single retroflex sound in many accents

You don’t need to imitate every fine detail, but getting the stress right (LAN-ge, for-KLA-ri-ngen, BAR-na) is important.