Final answer:
Option b, 'The fight was not given up by him even though he was badly bruised,' is the correct passive voice construction of the sentence provided.
Step-by-step explanation:
The correct passive voice construction of the sentence 'He did not give up the fight even though he was badly bruised' is represented by option b. This is because the action performed by the subject ('he') in the original sentence is being described as done to the object ('the fight'). The correct passive voice structure must include a form of the verb 'to be' and the past participle of the main verb 'give', which is 'given'.
Therefore, the only sentence adhering to this structure is: 'The fight was not given up by him even though he was badly bruised.'