The correct answers are If the burglar hadn't tripped over the mop bucket, he wouldn't have woken up the security guard. and The getaway driver might have escaped if he had remembered to put gas in the car.

These sentences correctly use the Third Conditional (If + past perfect, would/might/could have + past participle) to talk about unreal or contrary-to-fact situations in the past.

"If the thief didn't wear..." is incorrect because it uses the past simple instead of the past perfect ("hadn't worn").

"would had avoided" is incorrect because modals like "would" must be followed by the base verb "have", never "had".