Jeg læser teksten for anden gang.

Læser is the present tense of at læse.

In Danish, the present tense often covers both:

• I read the text
• I am reading the text

So Jeg læser teksten for anden gang can naturally mean I am reading the text for the second time. Danish does not usually need a separate progressive form like English am reading.

For most Danish verbs, the present tense is formed by adding -r to the infinitive.

• at læse = to read
• læser = read / am reading

This ending does not change with the subject:

• jeg læser
• du læser
• han læser

So Danish verbs are much simpler than English in this respect.

Because Danish usually makes a noun definite by adding the article to the end of the noun.

• en tekst = a text
• teksten = the text

So teksten is literally text + the.

This is very common in Danish. English speakers often expect a separate word like the, but Danish often attaches it instead.

Den tekst usually means something more like that text or a more contrastive that particular text.

For the ordinary meaning the text, Danish normally uses teksten.

A useful rule:

• plain definite noun: teksten
• more emphatic or demonstrative: den tekst
• with an adjective: den lange tekst = the long text

Here for is part of a fixed expression:

• for første gang = for the first time
• for anden gang = for the second time
• for tredje gang = for the third time

So you should learn for ... gang as a set pattern meaning for the ... time.

It does not mean for in the usual English sense here.

Because gang is a common-gender noun.

• en gang = a time / occasion

With common-gender nouns, second is anden. With neuter nouns, it would be andet.

So:

• for anden gang = for the second time
• det andet år = the second year

This is a gender agreement issue.

Because for anden gang is an idiomatic expression.

Danish says:

• for første gang
• for anden gang
• for tredje gang

So even though English has for the second time, Danish does not include den here.

If you said for den anden gang, it would sound wrong in this standard expression.

Gang here means time in the sense of an occurrence or occasion.

So:

• en gang = once / one time
• to gange = twice / two times
• anden gang = second time

This is a very common Danish word, and it appears in many expressions about repetition.

Yes. It follows a very normal Danish main-clause pattern:

• Jeg = subject
• læser = verb
• teksten = object
• for anden gang = adverbial phrase

So the structure is:

subject + verb + object + time/occurrence phrase

That is the most neutral order here.

Yes, but the meaning is slightly less specific.

• Jeg læser teksten igen = I am reading the text again
• Jeg læser teksten for anden gang = I am reading the text for the second time

Igen only says that it is happening another time. For anden gang tells you specifically that it is the second time.

So the sentence you were given is more precise.

Yes. In everyday writing, Danish often uses:

Jeg læser teksten for 2. gang.

That means exactly the same as for anden gang.

So:

• for anden gang = written out
• for 2. gang = same meaning, numeric form