Answer: In the mitochondria.
Explanation: The enzymes of fatty acid break down are located in the mitochondrial matrix. Fatty acid break down occurs in the mitochondria in a process known as beta oxidation. Beta oxidation involves the break down of fatty acids to acetyl CoA. Beta oxidation involves the oxidative removal of successive two carbon units in the form of acetyl CoA .
Acetyl CoA produced enters into the citric acid cycle for the generation of ATP.