Learn Russian: Со второй попытки её брату удалось сдать экзамен. - On the second attempt, her brother managed to pass the exam.

Удаваться / удаться acts as an impersonal verb here. It doesn't agree with the person doing the action. Instead, the logical subject goes in the dative case (брату), and the verb takes the default neuter singular form (удалось in the past tense) when followed by an infinitive like сдать.

Why does it say со второй instead of just с второй?

The preposition с changes to со to make pronunciation easier before words starting with certain double consonants, especially if the first consonant is в or ф. Since второй starts with вт, saying с второй would be a tongue-twister!

Doesn't сдавать экзамен mean 'to take an exam'? Why is it translated as 'to pass'?

This is a tricky difference in Russian verb aspects! The imperfective verb сдавать focuses on the process, meaning 'to take an exam'. The perfective verb сдать, used here, focuses on the result, meaning 'to pass an exam'. Because he succeeded, we use the perfective сдать.

Why are the words for 'second attempt' in the genitive case (второй попытки)?