Final answer:
The lesion causing acute onset of hemiballismus in the left upper and lower extremities is most likely located in the subthalamic nucleus or its surrounding structures
Step-by-step explanation:
An acute onset of hemiballismus of the left upper extremity (LUE) and left lower extremity (LLE) suggests damage to the subthalamic nucleus of the basal ganglia. In this condition, there is a hyperactive contralateral thalamocortical pathway, leading to involuntary flinging movements on one side of the body.
MRI is most likely to show a lesion located in the subthalamic nucleus or its surrounding structures, such as the internal capsule or basal ganglia.
It is important to note that a thorough clinical evaluation and additional diagnostic tests may be necessary to confirm the exact location of the lesion.