Final answer:
The correct way to express David's question in indirect speech is 'David asked Roger if he knew how to play darts.' This maintains the proper backshift of tense needed when the reporting verb is in the past tense.
Step-by-step explanation:
When converting a direct speech question to indirect speech, it is important to follow certain rules of backshifting tenses and pronouns. The correct way to express the sentence "Do you know how to play darts, Roger?" asked David in indirect speech is by using the past simple tense 'knew' to replace the present simple 'know' because the reporting verb 'asked' is in the past tense. Therefore, the correct form of the indirect speech here would be:
a) David asked Roger if he knew how to play darts.
The other options are incorrect because they either don't backshift the tense correctly (option 'b'), use an incorrect verb form (option 'c'), or do not accurately reflect the original question being asked (option 'd').