Billedet på forsiden af romanen er smukt.

Because billedet is the definite form: the picture.

• et billede = a picture
• billedet = the picture

Danish usually adds the definite article to the end of the noun instead of putting a separate word in front, as English does.

For the same reason: they are also in the definite singular form.

• en forside = a front page / a cover

• forsiden = the front page / the cover

• en roman = a novel
• romanen = the novel

So Danish often marks the by attaching -en or -et to the noun.

Because Danish nouns belong to different grammatical genders.

• et billede is a neuter noun, so the definite ending is -et → billedet
• en forside and en roman are common gender nouns, so the definite ending is -en → forsiden, romanen

This also affects adjectives later in the sentence.

Because smukt agrees with the noun billedet, which is neuter.

When an adjective describes a noun after er, Danish still usually shows agreement:

• en roman er smuk
• et billede er smukt

So here:

• billedet = neuter
• therefore smukt = the correct form

It means on the front/cover of the novel.

Breaking it down:

• på = on
• forsiden = the front page / the front side / the cover
• af = of
• romanen = the novel

So the whole phrase tells you where the picture is located: it is on the novel’s front cover.

Yes, both are possible.

This sentence uses an of-construction:

• forsiden af romanen = the front of the novel

A more compact possessive version is:

• romanens forside = the novel’s front / the novel’s cover

So you could also say:

• Billedet på romanens forside er smukt.

That is also natural Danish. The version with af is often a little more straightforward for learners.

Because Danish usually puts the definite article at the end of the noun.

English says:

• the picture
• the cover
• the novel

Danish says:

• billedet
• forsiden
• romanen

So the idea of the is already built into the noun form.

The structure is:

• Billedet på forsiden af romanen = subject
• er = verb
• smukt = adjective describing the subject

So literally:

• The picture on the cover of the novel
  • is
    • beautiful

This is a normal Danish main clause with the verb in second position.

In this sentence, with romanen, it most naturally means cover.

So forsiden af romanen is best understood as the front cover of the novel.

In other contexts, forside can also mean front page, for example with a newspaper or website. The exact meaning depends on context.

In the present tense, er is used for all persons:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• vi er = we are
• de er = they are

So Danish verbs are much simpler than English in this way: the verb does not change much depending on the subject.

In normal speech, the d in billedet is not pronounced like a clear English d.

A learner-friendly approximation is something like:

• BIL-uh-th

But pronunciation varies a bit by speaker and accent, and the final -et is often quite light. The important thing for beginners is:

• do not pronounce it like a strong English bill-ed-et
• the middle d is softened a lot

If you want, I can also break the whole sentence down word by word with pronunciation help.