Den første samtale gik godt, hvilket gjorde hende mere sikker på, at hun ville blive ansat.

Because samtale is a common-gender noun in Danish, not a neuter noun.

• Common gender takes den
• Neuter takes det

So:

• en samtale = a conversation / an interview
• den første samtale = the first conversation / interview

If the noun were neuter, you would use det første ... instead.

In this context, samtale very often means interview, especially a job interview.

So although the basic meaning of samtale is conversation, in a sentence about possibly being hired, den første samtale is very naturally understood as the first interview.

This is common in Danish:

• en jobsamtale = a job interview
• første samtale can be shorthand for første jobsamtale when the context is clear

Første is an ordinal number, meaning first. Ordinals in Danish often behave like adjectives, but første itself does not change form here.

So you get:

• den første samtale
• det første møde
• de første dage

Unlike many ordinary adjectives, første stays første.

Gå godt is a very common expression meaning to go well.

So:

• Samtalen gik godt = the interview went well

This matches English quite closely. Danish often uses gå in this way for how an event turns out.

For example:

• Det gik godt = It went well
• Eksamen gik dårligt = The exam went badly

Because godt is an adverb here, not an adjective.

In this sentence, godt describes how the interview went, not what the interview was.

Compare:

• Samtalen var god = The interview was good
  
  • god is an adjective describing samtalen
• Samtalen gik godt = The interview went well
  
  • godt is an adverb describing the verb phrase gik

This is very similar to English good vs well.

Here hvilket means which, and it refers to the whole previous idea, not just to one noun.

So:

• Den første samtale gik godt, hvilket ... means
• The first interview went well, which ...

In other words, hvilket refers to the fact that the first interview went well.

This is a very common Danish pattern:

• statement + , hvilket ...
• statement + , which ...

Because hvilket is the subject of that clause.

The structure is:

• hvilket = which
• gjorde = made

So literally:

• which made her more confident ...

You can think of it as:

• This fact made her more confident ...

That is why the verb comes directly after hvilket.

Because hende is the object form of the pronoun, while hun is the subject form.

Compare:

• hun = she
• hende = her

In this sentence, she is the person being affected by the action:

• hvilket gjorde hende mere sikker
  = which made her more confident

So Danish uses hende, just as English uses her, not she.

This is a useful Danish pattern:

• gøre + someone + adjective

So:

• gjorde hende mere sikker = made her more certain / more confident

Then sikker often takes på when it means sure/certain/confident about:

• Hun er sikker på noget = She is sure about something
• Hun er sikker på, at ... = She is sure that ...

So the full structure is:

• gjorde hende mere sikker på, at ...
• made her more certain/confident that ...

Because they do different jobs.

• på belongs with sikker
• at introduces the following clause

So:

• sikker på noget = sure about something
• sikker på, at hun ville blive ansat = sure/confident that she would be hired

This is normal Danish grammar. The combination på, at is very common after adjectives like sikker.

It means would be hired.

This has two important parts:

• ville = would
• blive ansat = be hired

So the sentence is talking about what she expected at that point in the past. It is not saying she definitely got the job; it says she felt more confident that it would happen.

Because the sentence is told from a past point of view.

The interview went well, and that past event made her feel more confident that she would be hired.

This is the same idea as English:

• present viewpoint: she will be hired
• past viewpoint: she would be hired

So ville here is the natural Danish choice for future seen from the past.

Blive ansat is a passive-style construction meaning to be hired or to get hired.

• ansætte = to hire
• ansat = hired / employed
• blive ansat = become hired / be hired

Using blive makes it clear that this is about the process or event of being hired.

Compare:

• Hun er ansat = She is employed
• Hun blev ansat = She was hired
• Hun ville blive ansat = She would be hired

So blive is very important here.

Because Danish punctuation traditionally uses commas to mark clause boundaries quite clearly.

In this sentence:

• comma before hvilket marks the start of a new clause
• comma before at marks the start of the at-clause

So the commas help show the structure:

• main clause: Den første samtale gik godt
• relative/comment clause: hvilket gjorde hende mere sikker på
• content clause: at hun ville blive ansat

You may sometimes notice slight differences in comma style depending on the system being used, but here the commas are completely normal and helpful.