Learn Hardcore Japanese: kadai ga owattaato, ongaku wo kikimasu. - I listen to music after I finish my assignments.

が marks the grammatical subject of the intransitive verb 終わる (“to finish”). If you used は, it would set 課題 as the topic with a contrast or background nuance. If you wanted to use を, you’d have to switch to the transitive verb 終える (“to complete”), as in 課題を終えたあと.

What does 終わったあと mean, and why is the verb in the past tense?

The pattern Verb (plain past) + あと means “after [verb]ing.” Using the past tense 終わった (“finished”) indicates that the action is completed before the next one happens.

Why is あと in hiragana and not written as the kanji 後?

After verbs, あと is commonly written in hiragana even though the kanji is 後. When あと follows a noun, you might see 後 (e.g. 学校の後), but after verbs, textbooks and native speakers often prefer the hiragana.

Do I need a particle like に or で after あと?

No particle is strictly necessary when あと functions as a time adverbial: 終わったあと、音楽を聞きます is perfectly correct. You can add に (終わったあとに) or で (終わったあとで) if you want to emphasize the exact timing or sound more natural in spoken Japanese, but both are optional here.

Can I say 終わったら instead of 終わったあと?

Yes. 終わったら、音楽を聞きます uses the conditional たら (“when/once”). 〜たら often implies immediacy or a condition, while 〜たあと is more neutral about timing. Both are correct and common.

Why is 音楽 followed by を?

The particle を marks 音楽 as the direct object of the transitive verb 聞く (“to listen [to]/hear”). In standard Japanese, you need を to show what you’re listening to.

Could I use 聴きます (with 聴) instead of 聞きます?

Yes. 聴く emphasizes active or attentive listening (e.g. appreciating music), while 聞く is more general (“hear/listen”). In everyday Japanese, 音楽を聞く with 聞 is more common, but 音楽を聴く is also perfectly acceptable.

Why does the verb 聞きます come at the end of the sentence?

Japanese typically follows Subject–Object–Verb order. After setting the scene with 課題が終わったあと (time phrase) and the object 音楽を, the main verb 聞きます naturally appears at the end.

How can I make this sentence more casual?

You can switch 聞きます to the plain form 聞く and drop the comma:
課題が終わったあと音楽を聞く。
In conversation, you might also say 課題終わったら音楽聞くよ。 with more contractions and colloquial particles.