In the question , some parts of the sentences have errors and some have none. Find out which part of a sentence has an error .The number of that part is the answer. If there is no error, then your answer is (4) i.e. No error.
By the time she had finished her work (1)/I had nearly given up (2)/all hope of arriving at the party in time. (3)/No error(4)

Answer

1

Explanation

Here, By the time she finished her work (Simple Past) ...... should be used.