Jeg kan godt lide billedet på forsiden af romanen.

Yes, kan normally means can, but kan lide is a very common fixed expression meaning to like.

So:

• Jeg kan lide kaffe = I like coffee
• Jeg kan lide billedet = I like the picture

You should learn kan lide as one unit. If you translate it word-for-word, it can seem strange, but idiomatically it just means like.

Godt is very often added with kan lide. It makes the sentence sound more natural in many contexts and can add a nuance like quite, really, or rather liking something.

Compare:

• Jeg kan lide billedet = I like the picture
• Jeg kan godt lide billedet = I quite/really like the picture

In many situations, both are possible. The version with godt is extremely common in everyday Danish.

Here godt is not describing a noun. It is functioning adverbially, modifying the verbal expression kan lide.

A useful pattern is:

• god = good
• godt = well / in a good way / adverb-like form

So in kan godt lide, the -t form is the natural one.

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

So:

• et billede = a picture

• billedet = the picture

• en forside = a front page / front cover

• forsiden = the front page / the front cover

• en roman = a novel
• romanen = the novel

This is one of the biggest differences from English. Instead of putting the before the noun, Danish often adds a definite ending to the noun itself.

The nouns are:

• et billede → billedet
• en forside → forsiden
• en roman → romanen

Danish has two grammatical genders:

• common gender: usually takes en in the indefinite form and -en in the definite form
• neuter: usually takes et in the indefinite form and -et in the definite form

So:

• billede is neuter: et billede, billedet
• forside is common gender: en forside, forsiden
• roman is common gender: en roman, romanen

Because the two prepositions do different jobs:

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

So the whole phrase means something like:

• the picture on the front cover
• the front cover of the novel

På is used because the picture is located on the surface of the cover.
Af is used to show that the cover belongs to or is part of the novel.

Yes. Both are correct.

• på forsiden af romanen
• på romanens forside

The second version uses the Danish -s genitive, similar to English the novel’s front cover.

A small difference in feel:

• på forsiden af romanen is very straightforward and common
• på romanens forside can sound a bit more compact or slightly more formal/written

Both are natural Danish.

The sentence breaks down like this:

• Jeg = subject
• kan = finite verb
• godt = adverb
• lide = infinitive/main verb
• billedet = direct object
• på forsiden af romanen = prepositional phrase describing billedet

So the structure is:

Subject + finite verb + adverb + infinitive + object + prepositional phrase

This is normal Danish main-clause word order.

Yes, often it would.

Main clause:

• Jeg kan godt lide billedet på forsiden af romanen.

Subordinate clause:

• ... fordi jeg godt kan lide billedet på forsiden af romanen.

Notice the difference:

• main clause: jeg kan godt lide
• subordinate clause: jeg godt kan lide

That is a very important Danish pattern: in subordinate clauses, sentence adverbs often come before the finite verb.

It is singular because the sentence refers to one specific picture.

Forms:

• et billede = a picture
• billedet = the picture
• billeder = pictures
• billederne = the pictures

If you wanted the plural, you could say:

• Jeg kan godt lide billederne på forsiden af romanen = I like the pictures on the front cover of the novel

Forsiden usually means the front side, the front page, or the front cover, depending on context.

With romanen, it most naturally means the front cover of the novel.

The same word can be used in other contexts too:

• forsiden af avisen = the front page of the newspaper
• forsiden af hjemmesiden = the front page/home page of the website
• forsiden af bogen = the front cover of the book

So the exact English translation depends on what kind of thing is being talked about.

Lide means like.
Elske means love.

So:

• Jeg kan godt lide billedet = I like the picture
• Jeg elsker billedet = I love the picture

For learners, kan lide is the everyday, neutral way to express liking something. Elske is much stronger.

A rough guide for an English speaker:

• jeg ≈ yai / yaiy with a soft beginning
• kan ≈ kahn
• godt ≈ something like got, but with a softer Danish sound
• lide ≈ LEE-thuh / LEE-the, with a very soft d
• billedet ≈ BIL-uh-leth or BIL-uh-le, depending on speech style
• forsiden ≈ FOR-see-then
• romanen ≈ ro-MA-nən

The exact pronunciation varies a bit by accent and speaking speed, and Danish pronunciation is often less phonetic than spelling suggests. If pronunciation is important for you, this is a sentence where listening to native audio is especially helpful.