A- primary motor cortex = wrong side of body (deficit of UMN on left side body)
B - Thalamus = sensory information conduit - motor deficits unlikely to originate from here
C - Pons - CNs 8,7,6,5, likely result in "locked in syndrome" or complete loss of motor function on right side + facial features.
D. Vermis - central body coordination. Damage results in ataxia
Not complete but maybe helpful..
Dysmetria ( also, dysdiadokinesia and intention tremor) is lateral cerebellum. (E).
Ataxia is a problem with the central cerebellum (D) or at least thats the best I could come up with.
Dysmetria is the lack of coordination of intended movements. Normally these movements are coordinated by the cerebellum. This is located specifically on the man's right side, not both sides, so only one lobe will be injured.
Dysmetria = discoordination of planned, voluntary movements (my own words for the different findings and used specifically to help me remember location) controlled by the posterior lobe of the hemisphere which does planned voluntary movement. Also, the hemisphere is the periphery of the cerebellum, and it deals with planned, voluntary movements of the periphery (i.e. limbs). I got this from this image with memory tips: https://www.medicowesome.com/2013/04/cerebellum-mnemonics.html.
Other helpful links:
Pretty detailed anatomy: http://www.fmritools.com/kdb/_Media/image002-3_med_hr.png
Interactive site all about the cerebellum (https://nba.uth.tmc.edu/neuroscience/m/s3/chapter05.html), but the most helpful picture for me was this one (https://nba.uth.tmc.edu/neuroscience/m/s3/images/copyright_marked_images/5-3_NEW.jpg)