Step 1: Lay out the tyrosine catabolic pathway in order: tyrosine is transaminated, then $p$-hydroxyphenylpyruvate is oxidised, and several steps later fumarylacetoacetate is finally split into fumarate and acetoacetate.
Step 2: Tyrosinosis, the type I and most severe tyrosinemia affecting liver and kidney, results from blocking that very last hydrolysis step, which is run by fumarylacetoacetate hydrolase.
Step 3: With this enzyme missing, the toxic intermediates fumarylacetoacetate and succinylacetone pile up and injure hepatic and renal tissue, fitting the clinical picture.
Step 4: Map the distractors to their own diseases: deficiency of tyrosine transaminase gives type II, deficiency of $p$-hydroxyphenylpyruvate dioxygenase gives type III, and tyrosine ligase is not part of the pathway.
\[\boxed{\text{Fumarylacetoacetate hydrolase}}\]