Den lange behandling fik hende til at tænke mere på sin krop.

Because behandling is a common-gender noun in Danish: en behandling.

For common-gender nouns, the singular definite article used before an adjective is den:

• en behandling = a treatment
• den lange behandling = the long treatment

If the noun were neuter (et-word), you would use det instead.

Because the noun phrase is definite: den lange behandling.

In Danish, adjectives usually take -e in definite forms:

• en lang behandling = a long treatment
• den lange behandling = the long treatment

So lang becomes lange because it is describing a definite noun.

In standard Danish, when a noun is definite and has an adjective before it, Danish normally uses:

• den/det/de + adjective + noun

So:

• behandlingen = the treatment
• den lange behandling = the long treatment

You do not normally combine the preposed definite article and the noun’s definite ending in this kind of phrase.

This is a very common Danish pattern:

få + someone + til at + infinitive

It means to make/get someone to do something.

So:

• fik hende til at tænke = made her think / caused her to think

Here:

• fik = made/got
• hende = her
• til at tænke = to think

The whole idea is that the treatment caused her to think more about her body.

Yes, få often means get, and fik is its past tense.

But få has several uses. In this sentence it is part of the causative construction:

• få nogen til at gøre noget = make/get someone to do something

So fik here does not mean simply got in the sense of receiving something. It means something closer to made or caused.

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

Compare:

• Hun tænker. = She thinks.
• Behandlingen fik hende til at tænke. = The treatment made her think.

In this sentence, she is not the grammatical subject of fik. The subject is den lange behandling. So Danish uses hende.

Because after til in this causative pattern, Danish normally uses at + infinitive:

• få nogen til at gøre noget
• fik hende til at tænke

So at tænke is the infinitive form, meaning to think.

This is just the standard structure of the expression.

Mere means more, and here it modifies the verb phrase tænke på sin krop.

So:

• tænke på sin krop = think about her body
• tænke mere på sin krop = think more about her body

It means the treatment increased how much she thought about her body.

Because Danish often uses tænke på for think about or think of.

So:

• tænke = think
• tænke på noget = think about something

In this sentence, på links the thinking to its topic:

• på sin krop = about her body

English sometimes uses think about, and Danish often does the same idea with tænke på.

Because Danish uses sin/sit/sine as a reflexive possessive when the possessor is the subject of the clause or the understood subject of the infinitive.

Here, in at tænke mere på sin krop, the understood subject of tænke is hende. So sin refers back to that same person.

So:

• sin krop = her own body

If you said hendes krop, it would often suggest someone else’s body, not her own.

Because krop is a common-gender noun: en krop.

The reflexive possessive agrees with the noun possessed:

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

So:

• sin krop = her own body
• but sit hus = her own house
• and sine hænder = her own hands

Not with exactly the same feel.

• tænke på usually means think about, with focus on what is in your mind
• tænke over often means reflect on or think over, with a stronger sense of consideration or analysis

So tænke mere på sin krop sounds natural for thinking more about her body in general.
If you used tænke mere over sin krop, it would sound more like reflect more on her body, which is a slightly different nuance.

The sentence is built like this:

• Den lange behandling = subject
• fik = verb
• hende = object
• til at tænke mere på sin krop = infinitive phrase explaining what she was made to do

So the structure is:

[Subject] + [Verb] + [Object] + [til at + infinitive phrase]

That is a very normal Danish sentence pattern.