Step 1: Recognise the syndrome. Crossed sensory loss, pain and temperature lost on the same side of the face but the opposite side of the body, is the hallmark of lateral medullary (Wallenberg) syndrome.
Step 2: Explain the crossed pattern. The spinal trigeminal nucleus serves the ipsilateral face, while the already crossed spinothalamic tract carries pain and temperature from the contralateral body. A lateral medullary lesion hits both, giving the crossed picture.
Step 3: Identify the vessel. The syndrome results most often from vertebral artery occlusion, and the named artery classically associated with it is the posterior inferior cerebellar artery (PICA).
Step 4: Other features. Wallenberg syndrome also causes vertigo, dysphagia, dysarthria, hoarseness, ataxia, and ipsilateral Horner syndrome. So the answer is PICA. Ref: Adams and Victor's Principles of Neurology, 11e.