Hærdningen ændrer ikke brillestyrken.

Because hærdningen is the definite singular form of hærdning. Danish usually adds the definite article to the end of the noun:

• hærdning = hardening
• hærdningen = the hardening

The base noun is related to the verb at hærde.

Ændrer is the present tense of at ændre. Danish present tense is very often formed with -r:

• at ændre = to change
• ændrer = changes / is changing / does change

So Hærdningen ændrer ikke... means The hardening does not change...

That is normal Danish main-clause word order. In a simple statement, Danish usually puts:

subject + finite verb + sentence adverb + object

So here:

• Hærdningen = subject
• ændrer = finite verb
• ikke = sentence adverb
• brillestyrken = object

That is why ikke comes after ændrer, not before it.

Because Danish normally writes compound nouns as one word. Brillestyrken is a compound:

• brille
  • styrke = brillestyrke

English often uses separate words where Danish uses a compound. This is one of the most important spelling patterns in Danish.

For the same reason as hærdningen: -en marks the definite singular.

• brillestyrke = glasses strength / prescription
• brillestyrken = the glasses strength / the prescription

In Danish compounds, the definite ending is added to the whole compound.

Because Danish often expresses the by adding an ending to the noun instead of using a separate word in front of it.

So:

• hærdning = hardening

• hærdningen = the hardening

• brillestyrke = prescription
• brillestyrken = the prescription

A separate article like den is not used here.

The letter æ is usually pronounced somewhat like the vowel in English bed, though not exactly the same.

So for an English speaker:

• hær- starts with an eh-type sound
• ænd- starts with the same kind of vowel

The important thing is not to pronounce æ like the a in day.

The sentence as written has very standard word order. But Danish can move other elements to the front, as long as the finite verb still stays in second position.

For example:

Normalt ændrer hærdningen ikke brillestyrken.

So the sentence structure can change, but Danish still follows the verb-second rule in main clauses.