A stroke victim has great difficulty moving his right hand and right leg. He also has trouble speaking. Which of his cerebral hemispheres is most likely to have been damaged

The correct answer is left cerebral hemisphere.

Explanation:

The left cerebral hemisphere of the brain is accountable for the motor control of the right side of the body, for sensory stimulus from the body’s right side, for analysis and calculations, for the speech, comprehension, and language, for the recognition of letters, words, and numbers, and for time and sequencing.  

The left cerebral hemisphere is accountable for the processing of the sensory information and motor information for the body’s right side. Thus, as left cerebral hemisphere monitors the movement of the body's right side, so, based on the extremity of the stroke, which may result in motor skill impairment or functional loss of the right side of the body, shows that the left side of the brain has got affected.