I approached this using the Rule of 4's. Patient has hoarseness, which is a CN 10 problem. CN 10 is located in the medulla. Patient also has decreased pain/temp to her left face and right body, which suggests impairment of spinothalamic tract and sensory to CN 5. These lesions are lateral. Thus, the lesion is at the lateral medulla.
ihst is lngWalbeer dosreynm - stkore dscuae by ostitrbocun of CPAI - os ttsah hyw ew egt ymsspotm fo yhadsgaip, no,ahrssees asbtne gag eefxlr (.p 052 AF)
just as an aside to what everyone saying, don't forget the 2 exceptions to the rule of 4s:
don't localize w/ CN5 (as seen here) b/c it is big and spans the pons and medulla
don't localize w/ the vestibular signs of CN8 b/c it is big. You CAN however localize with the sensoneural signs of CN8