Learn Hardcore Norwegian: Det er uten tvil hennes beste idé.

Because det is a dummy subject here, like English “it” in “It is…”. It does not agree with the gender of idé. If you said Den er uten tvil hennes beste idé, you’d be pointing back to a specific masculine noun already mentioned (“That one is, without a doubt, her best idea”). In the given sentence, det just introduces the statement: “It is, without a doubt, her best idea.”

Does Det er here mean “it is” or “there is”?

Here it means “it is,” linking the subject placeholder (det) to the description (hennes beste idé). Norwegian can use Det er for existential “there is/are” too (e.g., Det er en katt i hagen), but in this sentence it’s the copula “is.”

Can I move uten tvil to other positions?

Yes. Common options (all natural, with slightly different emphasis):

Det er uten tvil hennes beste idé. (Neutral emphasis.)
Det er hennes beste idé, uten tvil. (Tag-like afterthought.)
Uten tvil er det hennes beste idé. (Fronted for emphasis; remember V2: the finite verb er must stay in second position.) You could also say Det er definitivt hennes beste idé with the adverb definitivt.

Why is it uten tvil and not uten en tvil?

Uten tvil is a fixed expression meaning “without (a) doubt.” You can also say uten noen (som helst) tvil for extra emphasis. Uten en tvil is grammatical but sounds unnatural or overly literal in most contexts.

Why hennes and not sin?

Norwegian uses reflexive possessives (sin/sitt/sine) only when the possessor is the subject of the same clause. Here the subject is the dummy det, so you can’t use sin. Therefore: hennes beste idé, not sin beste idé. Compare:

Hun presenterte sin beste idé. (Here the subject is hun, so sin is correct.)
Det er hennes beste idé. (Subject is det, so use hennes.)

What’s the difference between henne and hennes?

henne = object pronoun “her” (I saw her): Jeg så henne.
hennes = possessive “her/hers” (her idea): hennes idé or idéen hennes.

Where can the possessive go: before or after the noun?

Both are possible, with a nuance:

Preposed: hennes beste idé (more written/formal, slightly more focus on the owner).
Postposed with definite noun: den beste ideen hennes / den beste idéen hennes (very common in speech and neutral). Do not say den hennes beste idé; the article and preposed possessive don’t combine like that.

Do superlatives require the definite form?

Attributive superlatives usually take the definite article and definite noun if there’s no preposed possessive: den beste ideen/idéen. But when a possessive is preposed, the noun stays morphologically indefinite: hennes beste idé (not “hennes beste idéen”). If you postpose the possessive instead, you return to the definite pattern: den beste ideen hennes/idéen hennes.

Why beste and not best?

beste is the attributive superlative used before a noun: hennes beste idé, den beste boken.
best is the predicative/adverbial form: Denne idéen er best. / Hun liker den best.

What gender is idé, and how do I inflect it?

Idé is a common-gender (en-word) noun in Bokmål.

Singular: en idé
Definite singular: idéen (also seen as ideen)
Plural: idéer (also ideer)
Definite plural: idéene (also ideene) Both the accented and unaccented spellings occur; see next question.

Do I have to write the accent in idé?

In Bokmål, both idé and ide are accepted. The accented form is traditional and helps signal stress (i‑DE) and distinguish it from other words, but many people omit accents in everyday writing. Be consistent with your choice. In Nynorsk, you’ll normally see idé (and utan tvil instead of uten tvil).

How do I pronounce the sentence?

Approximate IPA (Eastern Norwegian):

Det er uten tvil hennes beste idé ≈ [deː ær ˈʉːtən tviːl ˈhɛnːəs ˈbɛstə iˈdeː] Notes:
idé has final stress: i‑DE.
Long vowels in tvil [tviːl] and idé [iˈdeː].
uten has long u: [ˈʉːtən].

How would I say “It’s not her best idea”?

Place ikke after the verb and before the noun phrase:

Det er ikke hennes beste idé. Postposed variant also works:
Det er ikke den beste ideen/idéen hennes.

What are natural alternatives to uten tvil?

definitivt: Det er definitivt hennes beste idé.
helt klart: Det er helt klart hennes beste idé.
uten noen (som helst) tvil: stronger emphasis.