Learn Turkish: Yıllardır bütün duygularını kendi içine hapsetti. - For years, he confined all his emotions inside himself.

This is a compound verb made from the noun hapis (confinement) and the auxiliary verb etmek (to do). When they combine, the second vowel in hapis drops out. This is called vowel elision. According to Turkish spelling rules, if an auxiliary verb compound undergoes a sound change like vowel loss or consonant doubling, it must be written as a single joined word.

How do we know duygularını means his emotions and not your emotions?

The breakdown here is duygu + -lar (plural) + -ı (his) + -n- (buffer) + -ı (accusative). By coincidence, your emotions would look exactly the same: duygu + -lar + -ın (your) + -ı (accusative). You must rely on context to tell them apart. Here, the verb hapsetti (he confined) and the reflexive phrase kendi içine (inside himself) make it clear we are dealing with the third person.

Why does kendi içine take the dative case -e?

The verb hapsetmek (to confine or imprison) requires the dative case for the place where something is being confined. Even though English uses inside or in (which feels like it should be the locative case), Turkish treats this action as directing the emotions into a place. The word breaks down as iç (inside) + -i (his possessive) + -n- (buffer) + -e (dative direction).