Stroke (Left Middle Cerebral Artery Infarction): This is the most likely diagnosis given the combination of left hemi-anopsia (indicative of a visual field defect) and right facial weakness. The left middle cerebral artery supplies the left optic radiation, which, when damaged, can cause left hemi-anopsia, and also supplies the motor cortex controlling the right side of the face.

Multiple Sclerosis: This condition can cause a wide range of neurological symptoms, including visual disturbances and weakness. Optic neuritis, which can cause visual field defects, and lesions in the brainstem or spinal cord could explain the facial weakness.
Brain Tumor: A tumor in the left hemisphere of the brain could cause both visual field defects by compressing or infiltrating the optic radiation and facial weakness by affecting the motor pathways.

Pituitary Apoplexy: Although less common, pituitary apoplexy (a sudden hemorrhage or infarction of the pituitary gland) can cause sudden visual field defects, including hemi-anopsia, and can also lead to cranial nerve palsies, which might result in facial weakness if the nerves supplying the face are affected.
Cavernous Sinus Thrombosis: This is a rare but potentially life-threatening condition that can cause a variety of neurological symptoms, including visual disturbances and cranial nerve palsies, due to the thrombosis of the cavernous sinus.

Moyamoya Disease: A rare condition caused by narrowing or blockage of the internal carotid artery and its branches, leading to reduced blood flow to the brain. It can cause strokes, visual disturbances, and other neurological symptoms.
Susac Syndrome: A rare condition characterized by microangiopathic changes in the brain, retina, and cochlea, leading to a combination of neurological, visual, and auditory symptoms, including visual field defects and potentially facial weakness.