Anstatt die ganze Aufgabe abzuschreiben, unterstreiche ich nur die wichtigsten Wörter.

Anstatt means instead of. It introduces the idea of an alternative: one thing is done rather than another.

So here:

• Anstatt ... abzuschreiben = instead of copying ...
• unterstreiche ich ... = I underline ...

German often puts this kind of phrase at the beginning to set up the contrast first.

Here anstatt is introducing an infinitive construction, basically:

• anstatt + infinitive with zu

So:

• anstatt ... abzuschreiben

This is very common in German when you want to say instead of doing something.

You may also see statt used in similar ways.

Because after anstatt in this structure, German uses the zu-infinitive.

The verb is abschreiben = to copy out / copy down.
It is a separable verb:

• prefix: ab-
• base verb: schreiben

When a separable verb is used with zu, the zu goes between the prefix and the verb stem:

• abschreiben → abzuschreiben
• anzufangen
• mitzubringen
• aufzuschreiben

So abzuschreiben means to copy out in the infinitive with zu.

Because the sentence begins with an infinitive group:

• Anstatt die ganze Aufgabe abzuschreiben, ...

In modern German, infinitive constructions introduced by words like anstatt, ohne, and um are normally separated by a comma.

So the comma marks the end of the opening infinitive phrase before the main clause begins.

Aufgabe is a feminine noun, so in the accusative singular it takes:

• die Aufgabe

The adjective ganz follows the definite article die, so it gets the weak ending -e:

• die ganze Aufgabe

This whole phrase is the object of abschreiben:

• die ganze Aufgabe abschreiben = to copy the whole exercise/task

Because German main clauses follow the verb-second rule.

The finite verb must come in the second position. The sentence starts with the infinitive phrase:

• Anstatt die ganze Aufgabe abzuschreiben

That entire phrase counts as position 1. So the conjugated verb must come next:

• unterstreiche = position 2
• ich comes after it

That is why you get:

• Anstatt ..., unterstreiche ich ...

and not:

• Anstatt ..., ich unterstreiche ...

Because unterstreiche is the finite verb of the main clause, and in a normal German main clause the finite verb goes in second position.

The verb goes to the end in subordinate clauses, but this is not a subordinate clause after the comma. It is the main clause:

• unterstreiche ich nur die wichtigsten Wörter

So the structure is:

1. opening phrase: Anstatt die ganze Aufgabe abzuschreiben
2. finite verb: unterstreiche
3. subject: ich
4. rest of the sentence

Nur means only, and here it modifies the object phrase:

• nur die wichtigsten Wörter = only the most important words

Its placement shows what is limited. The idea is not that the speaker only underlines, but that they underline only the most important words.

Because Wörter is plural.

The noun is:

• singular: das Wort
• plural: die Wörter

With the definite article die in the plural, the adjective takes the weak ending -en:

• die wichtigsten Wörter

Also, wichtigsten is the superlative form of wichtig:

• wichtig = important
• wichtiger = more important
• am wichtigsten / der/die/das wichtigste = most important

So die wichtigsten Wörter means the most important words.

German has two plural forms that can both appear:

• Wörter usually refers to individual words as separate units
• Worte often refers more to words as an utterance, statement, or saying

Here the meaning is clearly individual vocabulary items in a text, so Wörter is the natural choice:

• die wichtigsten Wörter = the most important words

Aufgabe can mean several related things depending on context:

• task
• exercise
• assignment
• sometimes homework task

In this sentence, it most likely means an exercise or task from class or a worksheet.

Not always. Abschreiben often means:

• to copy out
• to copy down
• to write something out from another source

Depending on context, it can even suggest copying someone else’s work, like cheating. But in a neutral learning context, it often just means copying text from a board, book, or worksheet.

Yes, very often statt and anstatt are both possible.

For example:

• Statt die ganze Aufgabe abzuschreiben, ...
• Anstatt die ganze Aufgabe abzuschreiben, ...

Both mean instead of copying the whole exercise, ...

In everyday German, statt is often a bit more common and shorter, but anstatt is perfectly correct.

It is neutral standard German. Nothing in it is especially formal or especially casual.

You could use a sentence like this:

• in class
• in homework instructions
• in conversation about study methods

So it sounds completely normal in everyday standard German.