Vi drøfter bogvalget.

Drøfter is the present tense form of the verb drøfte, which means to discuss or to deliberate.

• at drøfte = to discuss
• vi drøfter = we discuss / we are discussing

In Danish, the present tense is often made by adding -r to the infinitive:

• drøfte → drøfter

So Vi drøfter bogvalget is in the present tense.

They are close, but not always identical in tone.

• drøfte often sounds a bit more neutral, careful, or formal: to discuss, to consider
• diskutere can also mean to discuss, but sometimes it can sound a bit more like argue or debate, depending on context

So Vi drøfter bogvalget suggests calmly discussing the book choice, not necessarily arguing about it.

Because Danish, like German, very often forms compound nouns by writing them as a single word.

Here:

• bog = book
• valg = choice / selection

Together:

• bogvalg = book choice / choice of book

Then the definite ending is added:

• bogvalget = the book choice

Writing it as two words would usually be wrong in standard Danish.

The ending -et marks the noun as definite singular, meaning the.

So:

• bogvalg = a book choice / book choice
• bogvalget = the book choice

In Danish, you often do not use a separate word for the before the noun. Instead, the definiteness is added to the end of the noun.

Because in Danish, a noun usually shows definiteness with an ending, not with a separate article in front.

Compare:

• en bog = a book
• bogen = the book

And here:

• bogvalg = book choice
• bogvalget = the book choice

So bogvalget already includes the meaning of the. You do not need another word before it.

In Danish compounds, the last part of the compound determines the grammar.

The last part here is valg:

• et valg = a choice

Because valg is a neuter noun (it takes et), the whole compound is also neuter:

• et bogvalg
• bogvalget

So even though bog is part of the word, the grammatical gender comes from valg, not bog.

The word order is the normal Danish main-clause pattern:

• Vi = subject
• drøfter = verb
• bogvalget = object

So the structure is:

Subject + Verb + Object

This is very similar to English:

• We discuss the book choice

You would usually put ikke after the verb in a main clause:

• Vi drøfter ikke bogvalget.

So the pattern is:

Subject + Verb + ikke + Object

This is a very common placement for ikke in simple main clauses.

Yes, that is possible in some contexts.

• bogvalg = book choice
• valg af bog = choice of book

The compound bogvalg is compact and natural, especially in formal or written style.
The phrase valg af bog is also understandable and may sound a little more explanatory.

So Danish often has both options:

• a compound noun
• or a noun + prepositional phrase

A rough guide is:

• drøfter ≈ DRURF-ter or DRUF-ter, depending on accent and how exact you want to be

A few useful notes:

• ø is a front rounded vowel that English does not really have
• the r in Danish is not pronounced like a strong English r
• the ending -er in verbs is often pronounced quite lightly

If you want to sound natural, the hardest part is usually the vowel ø.