Han så flov ud, da hans søster sagde, at alle kunne høre, hvad de diskuterede i køkkenet.

In this sentence, så is not the adverb så meaning so/then. It is the past tense of se.

The key expression is at se ... ud, which means to look / to appear.

So:

• Han ser flov ud = He looks embarrassed.
• Han så flov ud = He looked embarrassed.

In a main clause, Danish often splits this expression:

• Han så flov ud

The full verb expression is still se ud.

Yes, but it changes the nuance.

• Han var flov = He was embarrassed.
• Han så flov ud = He looked embarrassed / He seemed embarrassed.

So var flov states his emotional state more directly, while så flov ud describes how he appeared to others.

Here da means when, referring to a specific event in the past.

• da hans søster sagde ... = when his sister said ...

This is different from:

• når = when, in general or for repeated events
• fordi = because

So in this sentence, da is correct because the sentence describes one past moment.

Because sin/sit/sine refers back to the subject of the same clause.

In the clause:

• da hans søster sagde ...

the subject is hans søster, not han.

So sin søster would have to refer back to the subject of that clause, which would not make sense here. Danish therefore uses hans to mean his.

A useful rule:

• use sin/sit/sine only when the possessor is the subject of that same clause
• otherwise use hans/hendes/deres etc.

Here at means that, not to.

So:

• hun sagde, at ... = she said that ...

Danish at has two common jobs:

1. Infinitive marker:

   • at høre = to hear

2. Conjunction meaning that:

   • sagde, at alle kunne høre ... = said that everyone could hear ...

In your sentence, it is the second one.

Because modal verbs in Danish normally take a bare infinitive.

So you say:

• kunne høre
• ville gå
• skulle arbejde
• måtte vente

not:

• kunne at høre

This is similar to English:

• could hear
• not could to hear

Yes, here de means they.

In:

• hvad de diskuterede
  = what they were discussing

it is the subject of the clause, so standard written Danish uses de.

Important distinctions:

• de = they
• dem = them
• De with a capital letter can be a formal you in older or very formal language

In this sentence, it is just ordinary de = they.

Because this is an embedded question or content clause:

• hvad de diskuterede = what they were discussing

After verbs like høre, vide, se, fortælle, Danish often uses words like:

• hvad = what
• hvem = who
• hvor = where
• hvornår = when

So høre, hvad de diskuterede means hear what they were discussing.

Because Danish usually uses the simple past where English often uses a past progressive.

So:

• de diskuterede can mean they discussed or they were discussing, depending on context.

Danish does have ways to emphasize ongoing action, but it does not need a special progressive form as often as English does.

So hvad de diskuterede is a perfectly natural way to express what they were discussing.

Because køkkenet means the kitchen.

• et køkken = a kitchen
• køkkenet = the kitchen

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

• bogen = the book
• huset = the house
• køkkenet = the kitchen

And i means in.

So:

• i køkkenet = in the kitchen

Because Danish writing often places commas around subordinate clauses.

This sentence contains several clauses:

• Han så flov ud
• da hans søster sagde
• at alle kunne høre
• hvad de diskuterede i køkkenet

In standard Danish punctuation, commas commonly mark where these subordinate clauses begin.

So the commas help show the structure of the sentence, not just pauses in speech.

This sentence is a good example of the difference between main clause and subordinate clause word order.

1. Main clause

• Han så flov ud

Danish main clauses normally follow the V2 rule: the finite verb comes in the second position.

Here:

• Han = subject
• så = finite verb
• flov = complement
• ud = particle from se ud

2. Subordinate clauses

• da hans søster sagde
• at alle kunne høre
• hvad de diskuterede i køkkenet

In subordinate clauses, Danish does not use the same V2 pattern. The subject normally comes before the verb in a more straightforward way:

• hans søster sagde
• alle kunne høre
• de diskuterede

So a useful takeaway is:

• main clause: often V2
• subordinate clause: more regular subject + verb order

This difference is one of the most important parts of Danish sentence structure.