The correct option is B have damaged
Let’s examine the sentence: ‘Would Bruce ____ his car if he had driven slowly?’ The sentence questions an unreal situation that actually did not happen. By reading the sentence, we can deduce that Bruce did not drive slowly. The sentence questions the unreal and imaginary situation of what would have happened if Bruce had driven his car slowly. The reality as can be understood from the sentence is that Bruce damaged his car by driving fast and presumably getting into an accident. So the sentence makes use of the third conditional.
The third conditional is used to talk about 'impossible' conditions.
Third conditional structure is: Would have + If + past perfect
Now, when we examine the options against the structure, only Option C meets the condition of the sentence with third conditional having the verb ‘would have.’ Here ‘would’ is used at the beginning of the sentence due to its question form. Hence, Option C is the correct answer.
Options A, B and D cannot be used as they would make the sentence grammatically incorrect.