Learn Hardcore Danish: Min bror glemmer sin billet, men han finder den igen. - My brother forgets his ticket, but he finds it again.

Because sin/sit/sine is the reflexive possessive and refers back to the subject of the same clause. Here the subject is Min bror, so sin billet means “his own ticket.” If you used hans, it would normally refer to another male, not the subject.

Min bror glemmer sin billet = My brother forgets his own ticket.
Min bror glemmer hans billet = My brother forgets another man’s ticket. In embedded clauses the same rule holds: Min søster siger, at min bror glemmer sin billet (his own) vs. … glemmer hans billet (someone else’s).

How do I pick min, mit, or mine? Why Min bror, not Mit bror?

It depends on the noun’s grammatical gender/number:

min
- common gender (en-words): min bror (en bror), min bil (en bil)
mit
- neuter (et-words): mit hus (et hus)
mine
- all plurals: mine brødre, mine huse Since bror is an en-word, you use min.

Why is it den and not det in han finder den igen?

The object pronoun agrees with the gender of the noun it replaces. Billet is an en-word (en billet), so the pronoun is den. If the noun were neuter (et-word), you’d use det.

Why is there a comma before men?

Danish normally places a comma before coordinating conjunctions like men when they join two main clauses. Here, both sides could stand as sentences on their own, so the comma is standard: …, men …

Can I leave out the subject han in the second clause?

No. Danish generally requires an explicit subject in each finite clause. So you say: …, men han finder den igen. Omitting han (…, men finder den igen) sounds like a headline or note, not standard sentence grammar.

Why is igen at the very end? Could I say han finder igen den?

With a short object pronoun like den, the natural order is verb + object pronoun + adverb: finder den igen. The version finder igen den is unidiomatic. If you use a full noun instead of a pronoun, both are possible, but the default is still to place igen at the end:

Han finder sin billet igen (neutral, very common).
Han finder igen sin billet (possible, puts a bit more focus on the repetition).

Could I use sine instead of sin?

Not here. Sine is the plural reflexive form. Use:

sin with en-words (singular): sin billet
sit with et-words (singular): sit kort
sine with plurals: sine billetter

Why isn’t it billetten (definite) after a possessive?

In Danish, a possessive normally takes an indefinite noun: min bog, hans telefon, sin billet. You do not add the noun’s definite ending at the same time (so not “min bogen” or “sin billetten”). If you want emphasis, you can add egen: sin egen billet (still indefinite).

What’s the difference between glemme and miste?

glemme = to forget (often to leave behind by mistake): Han glemmer sin billet (he forgets/left his ticket).
miste = to lose (to no longer have, it’s gone): Han mister sin billet (he loses his ticket). Your sentence says he forgot it but later found it again.

Does the present tense (glemmer, finder) describe a one-off event or a habit? How would I say it in the past?

Danish present can be used for current, habitual, or narrative actions. Context decides. For a past, single event use preterite:

Min bror glemte sin billet, men han fandt den igen. You can also use the present perfect for a result up to now:
Min bror har glemt sin billet, men han har fundet den igen.

Can I omit den and just say han finder igen?

No. finde is transitive here and needs its object. Han finder den igen is the normal way to say “he finds it again.” Without den, the sentence is incomplete or means something else.

What if the noun were neuter? How would the sentence change?

You’d switch both the reflexive possessive and the object pronoun:

Min bror glemmer sit kort, men han finder det igen. (et kort → sit; pronoun det for neuter.)

Can I add så after men to mean “but then”?

Yes. …, men så finder han den igen adds a clear sense of sequence (“but then he finds it again”). It’s natural and common in narratives.

Does igen modify finde or glemme? How do I say “he forgets it again”?

In the given sentence, igen modifies finder (he finds it again). To say he forgets it again, move igen into the first clause:

Han glemmer igen sin billet. You can also front it for emphasis: Igen glemmer han sin billet.