Learn Turkish: Bireylerin sorununu hafifsemiş. - He apparently took the individuals' problem lightly.

This sentence uses the suffix -(I)mse (or just -se after certain words), which attaches to adjectives or nouns to mean "to perceive as [adjective]" or "to treat as [noun]". Here, it attaches to hafif (light) to create hafifsemek—literally "to perceive as light," meaning to take something lightly or to underestimate it. Notice that with hafif, the connecting vowel drops, so we use -se rather than -imse.

Why does sorununu need the accusative case here?

Verbs derived with the -(I)mse suffix describe an attitude directed at something, which makes them transitive (they take a direct object). Because the specific thing being taken lightly is "the individuals' problem", the object requires the accusative case to show it is the direct receiver of the action.

Can you break down the stack of suffixes on sorununu?

Sure! It is part of the genitive-possessive phrase bireylerin sorunu (the individuals' problem). The breakdown is sorun (problem) + -u (3rd person possessive, linking it to the individuals) + -n- (a buffer letter always used when adding a case marker right after a possessive suffix) + -u (the accusative case marker).

What adds the meaning of "apparently" in the English translation?