Op de thuiswerkdag werken wij thuis.

Dutch normally uses op with days and specific day-like occasions.

So just as you say:

• op maandag = on Monday
• op die dag = on that day

you also get:

• op de thuiswerkdag = on the work-from-home day

Here thuiswerkdag is being treated as a specific day.

This is because of the Dutch verb-second rule.

In a main clause, the finite verb usually comes in the second position. Here, the first part of the sentence is:

Op de thuiswerkdag

So the verb must come next:

Op de thuiswerkdag werken wij thuis.

If you started with the subject instead, you would get normal subject-first order:

Wij werken thuis op de thuiswerkdag.

Both are grammatical, but the original sentence puts emphasis first on when it happens.

Thuiswerkdag is a compound noun, which is very common in Dutch.

It is made from:

• thuis = home / at home
• werk = work
• dag = day

Together, it means something like work-from-home day or home-working day.

Dutch often combines ideas into one long word where English would use several separate words.

Because the main noun in the compound is dag, and dag is a de-word.

A useful rule is that in Dutch compound nouns, the last part usually determines the gender/article.

So:

• de dag
• therefore de thuiswerkdag

Thuis here means at home.

It is an adverb, not a noun. In Dutch, adverbs of place often come later in the sentence, so werken wij thuis is normal.

Also, thuis is not the same as huis:

• thuis = at home
• naar huis = home / to home
• in huis = in the house

So wij werken thuis means we work at home.

It can feel repetitive to an English speaker, but it is perfectly natural.

• thuiswerkdag tells you what kind of day it is
• thuis tells you where the working happens

So the structure is basically:

On the work-from-home day, we work at home.

That repetition is acceptable because the first thuis is part of a noun, while the second thuis is an adverb.

Yes. In everyday Dutch, we is very common and often sounds more natural in speech.

So you could say:

Op de thuiswerkdag werken we thuis.

Wij is also correct, but it can sound a bit more formal, careful, or emphatic.

Yes, the verb thuiswerken exists.

Its dictionary form is written as one word:

• thuiswerken = to work from home

But in a normal main clause, it often appears split:

• Wij werken thuis.

That is because it behaves like a separable verb.

Compare:

• infinitive: thuiswerken
• main clause: wij werken thuis
• subordinate clause: omdat wij thuiswerken

So the sentence is consistent with that pattern.

Dutch present tense often covers both ideas.

So werken can mean:

• work in a general or habitual sense
• are working if the context is about what is happening now

Without extra context, this sentence often sounds like a general routine or schedule:

On the work-from-home day, we work at home.

Yes.

• op de thuiswerkdag = on the specific/known work-from-home day
• op een thuiswerkdag = on a work-from-home day, in general
• op thuiswerkdagen = on work-from-home days, in general/plural

So the original sentence suggests there is a particular home-working day that both speaker and listener know about.