Instruktøren beder hende sige den samme replik langsommere, så publikum kan høre hvert ord.

Instruktøren means the director. Danish often adds the definite article to the end of the noun instead of using a separate word like English the.

• en instruktør = a director
• instruktøren = the director

So -en is the definite ending here.

Because hende is the object form, like English her.

• hun = she
• hende = her

In this sentence, the director is asking her to do something, so Danish uses hende:

• Instruktøren beder hende ... = The director asks her ...

After bede nogen gøre noget meaning ask someone to do something, Danish normally uses the bare infinitive, without at.

So:

• bede hende sige det = ask her to say it
• not usually bede hende at sige det

This is a common pattern:

• Jeg bad ham komme = I asked him to come
• Læreren bad os vente = The teacher asked us to wait

It follows this pattern:

bede + person + infinitive

So here:

• beder = asks
• hende = her
• sige = say

Literally, it works like: The director asks her say...

But in natural English, that becomes: The director asks her to say...

This is a very useful Danish structure to learn.

Den samme means the same.

Danish usually says:

• den samme replik = the same line
• det samme problem = the same problem

Just samme replik can exist in some contexts, but den samme is the standard full expression when you mean the same in a specific sense.

Because replik is a common-gender noun, Danish uses den:

• den samme replik

If it were a neuter noun, it would be det samme.

Because den samme replik is one of those Danish structures where definiteness is shown by the article-like word in front, not by adding the definite ending to the noun.

Compare:

• replikken = the line
• den samme replik = the same line

After words like samme, første, sidste, and many adjectives in similar structures, Danish often uses:

• den/det/de + adjective + noun

So den samme replik is correct, not den samme replikken.

Langsommere is the comparative form of langsomt or langsom and means more slowly or slower.

Here it is used adverbially, describing how she should say the line:

• sige ... langsommere = say ... more slowly

Compare:

• langsom = slow
• langsomt = slowly
• langsommere = more slowly / slower

In English, we would usually say more slowly, but Danish commonly uses the comparative form like this.

Here så means so that.

• ..., så publikum kan høre hvert ord
  = ..., so that the audience can hear every word

This introduces a purpose or result.

Do not confuse this with other meanings of så, such as:

• then
• so
• very, in some contexts

In this sentence, så connects the first part to the purpose of speaking more slowly.

Because after så meaning so that, Danish usually keeps normal subordinate-clause word order.

That means:

• subject first: publikum
• then the modal verb: kan
• then the main verb: høre

So:

• så publikum kan høre hvert ord

This is different from main clause word order, where the verb often comes before the subject after another element.

Because kan is a modal verb meaning can, and modal verbs are followed by the infinitive form of the main verb.

So:

• kan = can
• høre = hear

Together:

• kan høre = can hear

This is very common in Danish:

• jeg kan se = I can see
• hun vil komme = she wants to come
• de skal gå = they must go

Hvert ord means each word or every word.

It focuses on individual words one by one:

• hvert ord = every single word

By contrast:

• alle ordene = all the words

Both can make sense, but hvert ord stresses clarity more strongly, which fits the sentence well.

Also note:

• hvert is used because ord is a neuter noun: et ord
• common-gender nouns would use hver

Examples:

• hver dag = every day
• hvert ord = every word

In Danish, publikum is a collective noun, like the audience in English. It refers to a group, but grammatically it is usually treated as singular.

So Danish says:

• publikum kan høre = the audience can hear

not something like publikum kan høre with a plural verb distinction, because Danish verbs do not change for singular and plural anyway. But the noun itself is grammatically singular in form.

Yes, replik is a very common word for a spoken line in a play, film, or script.

So:

• den samme replik = the same line

It can also mean a reply or retort in some contexts, depending on the situation. In a theatre or film context, replik is exactly the kind of word a learner should expect here.

Not naturally here. With bede, Danish normally uses the direct pattern:

• bede nogen gøre noget

So:

• Instruktøren beder hende sige ...

Using til at would sound wrong or at least unnatural in this structure.

A good rule is:

• bede nogen om noget = ask someone for something
• bede nogen gøre noget = ask someone to do something

This sentence is clearly the second type.