Learn Hardcore Korean: sueop hue balpyoreul junbihaeyo. - I prepare a presentation after class.

수업 means “class” or “lesson,” 후 means “after,” and -에 is a particle that marks a point in time. Put together, 수업 후에 literally means “after class.”

Why do we use -에 after 후? Can I drop it?

The particle -에 turns 후 into a time adverbial (“at the time after”). Without -에, the phrase sounds like a bare noun phrase and is less natural for indicating when something happens. In casual speech you might hear 수업 후 발표를 준비해요, but it’s more standard to keep -에: 수업 후에 발표를 준비해요.

Can I say 수업이 끝난 후에 instead of 수업 후에?

Yes. 수업이 끝난 후에 adds the verb 끝나다 (“to end”) plus the modifier -ㄴ to form a relative clause, literally “after the class has ended.” It’s slightly more explicit but means the same thing as 수업 후에.

What does 발표를 준비해요 mean, and why is there a -를 after 발표?

발표 is a noun meaning “presentation” or “speech,” and 준비해요 means “(I) prepare.” Because 발표 is the direct object of 준비하다, you attach the object particle -를 (used after vowel-final nouns) to mark “presentation” as what’s being prepared.