Learn Turkish: Bu problemi çözmeye çabaladın mı? - Did you try hard to solve this problem?

The verb çabalamak (to try hard / to strive) requires the action you are striving towards to take the dative case (meaning 'to' or 'towards'). To do this, we drop the -k from çözmek to get the verbal noun çözme (solving). Then we add the buffer letter -y- and the dative ending -e, giving us çözmeye. You can think of it literally as 'towards solving'.

Why does problem have an -i at the end?

Because it is the specific direct object of the verb çözmek (to solve). The word bu (this) makes it a specific item. Whenever you point out a specific object being acted upon ('this problem' rather than just 'a problem'), it needs the accusative case ending, which is -i here.

Why use çabaladın instead of çalıştın or denedin for 'did you try'?

While denemek means 'to test out' or 'attempt', and çalışmak is the standard word for 'to try' or 'to work', çabalamak carries the feeling of a real struggle or making a strenuous effort. That is why the English translation specifically says 'try hard'.

How does the word çabaladın break down grammatically?