Final answer:
Damage to the left frontal lobe (option A) is most likely the cause of Darryl's inability to produce speech after experiencing a stroke.
Step-by-step explanation:
Damage to the left frontal lobe (option A) is most likely the cause of Darryl's inability to produce speech after experiencing a stroke. Broca's area, which is located in the left frontal lobe, is responsible for the motor commands necessary for speech production. When this area is damaged, individuals often have difficulty speaking and forming meaningful language.
In contrast, damage to the right temporal lobe (option D) would affect the understanding of figurative aspects of speech, nonverbal aspects of speech, and emotional expression in speech, but it is not directly involved in speech production.
Therefore, based on Darryl's symptoms, the most likely part of his brain that has sustained damage is the lower left frontal lobe (option A).