Learn Turkish: Olumsuz şartlara ve yorgunluğa rağmen çok çaba gösterdiler. - Despite the negative conditions and tiredness, they showed a lot of effort.

The postposition rağmen (despite) always requires the word before it to be in the dative case (-(y)e / -(y)a). When you have multiple items joined by ve (and), it is standard in Turkish to attach the required case suffix to every noun in the list. That is why we see both şartlara and yorgunluğa.

Why is it yorgunluğa instead of yorgunluka?

The base word for tiredness is yorgunluk, which ends in the hard consonant k. When we add a suffix starting with a vowel (like the dative -a), the k undergoes consonant mutation and softens into a ğ.

What does çaba göstermek mean, and how is it different from çalışmak?

Çaba göstermek literally means to show effort or to make an effort. While you could use çalışmak to mean to work or to try, çaba göstermek emphasizes the specific exertion of energy and willpower, especially when overcoming difficult circumstances like in this sentence.

Where is the word for they in this sentence?