Step 1: Catecholamine biosynthesis runs tyrosine to dopa to dopamine to norepinephrine, and the very last conversion adds a methyl group to make epinephrine.
Step 2: The enzyme that carries out this methylation is phenylethanolamine N-methyltransferase, found mainly in the adrenal medulla.
Step 3: Like other methyltransferases, this enzyme cannot work without a methyl group source. S-adenosyl methionine serves as the universal methyl donor and supplies that group for the norepinephrine to epinephrine step.
Step 4: Arginine, phenylalanine, and any dehydrogenase do not provide the methyl group for this reaction, so the correct choice is S-adenosyl methionine.
\[\boxed{\text{S-adenosyl methionine}}\]