Hvis beskeden lyder uformel, skriver hun en mere formel email til sin chef.

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

In this sentence, the Hvis-clause comes first:

Hvis beskeden lyder uformel

That whole clause takes the first position, so in the main clause the verb must come before the subject:

skriver hun en mere formel email til sin chef

So the pattern is:

• Hvis ... , skriver hun ...
• not Hvis ... , hun skriver ...

This inversion is very common in Danish when something other than the subject comes first.

Lyder means sounds. So beskeden lyder uformel means the message sounds informal or comes across as informal.

That is slightly different from er uformel, which would mean the message is informal in a more direct, objective way.

So:

• lyder uformel = seems/sounds informal
• er uformel = is informal

Danish often uses lyde in the same kind of places where English uses sound.

Beskeden is the definite form of besked, so it means the message.

In Danish, the definite form is often used where English might say the message or sometimes even just speak more generally depending on context. Here it suggests a specific message that both speaker and listener can identify from the situation.

Forms:

• en besked = a message
• beskeden = the message

So Hvis beskeden lyder uformel is literally If the message sounds informal.

Because of how adjective agreement works in Danish.

In beskeden lyder uformel, the adjective is used predicatively after the verb lyder. Predicative adjectives agree with the noun:

• common gender singular: uformel
• neuter singular: uformelt
• plural/definite: uformelle

Since beskeden is a common-gender singular noun, the form is uformel.

In en mere formel email, the adjective is used before an en-word in the indefinite singular, so the basic form is also used:

• en formel email

That is why both adjectives appear in the basic form here.

Many Danish adjectives form the comparative with -ere, but others often use mere + adjective, especially longer or more learned-looking adjectives.

So:

• mere formel = more formal

This is very natural Danish.

You may sometimes see both patterns in Danish with some adjectives, but with formel, mere formel is the standard and safest choice for a learner.

Because sin/sit/sine is the reflexive possessive. It is used when the possessor is the subject of the clause.

Here, the subject is hun, and the boss belongs to her, so Danish uses sin:

• hun skriver ... til sin chef = she writes ... to her own boss

If you used hendes chef, it would usually mean another woman's boss, not the subject's own boss.

So the contrast is:

• Hun skriver til sin chef = to her own boss
• Hun skriver til hendes chef = to that other woman's boss

Because sin/sit/sine must agree with the noun being possessed, not with the owner.

The noun here is chef, which is a common-gender singular noun, so the correct form is sin.

Compare:

• sin chef = her/his own boss
• sit arbejde = her/his own work
• sine kolleger = her/his own colleagues

So the choice depends on the possessed noun:

• common gender singular → sin
• neuter singular → sit
• plural → sine

Yes. You could say:

Hvis beskeden lyder uformel, så skriver hun en mere formel email til sin chef.

The så means then. It is often optional after an if-clause in Danish.

So both are possible:

• Hvis ..., skriver hun ...
• Hvis ..., så skriver hun ...

Without så, the sentence is still completely natural.

Yes, email is widely understood and used in Danish. You may also see:

• e-mail
• sometimes mail in informal language

All of these occur, but email is very common in everyday writing.

Also, it takes en:

• en email
• emailen = the email

So en mere formel email is perfectly natural.

It can most naturally be read as a general rule, habit, or typical reaction:

If the message sounds informal, she writes a more formal email to her boss.

Danish present tense often works this way, just like English present tense can in conditional or habitual statements.

So skriver here does not have to mean she is doing it right now. It can mean that this is what she generally does in that situation.

Here hvis means if and introduces a condition.

So the structure is:

• Hvis X, Y
• If X, then Y

In this sentence:

• condition: beskeden lyder uformel
• result: skriver hun en mere formel email til sin chef

So hvis is functioning just like English if.