β-oxidation can occur in

β-oxidation can occur in Mitochondria and Peroxisomes.
Beta-oxidation is the catabolic process by which fatty acid molecules are broken down in the cytosol in prokaryotes and in the mitochondria in eukaryotes to generate acetyl-CoA, which enters the citric acid cycle, and NADH and FADH₂, which are co-enzymes used in the electron transport chain.
Mitochondria catalyze the beta-oxidation of the bulk of short-, medium-, and long-chain fatty acids derived from diet, and this pathway constitutes the major process by which fatty acids are oxidized to generate energy.