• Peroxisomal Fatty Acid $\beta$-Oxidation:
• Very long-chain fatty acids (VLCFAs, $\ge C_{22}$) and branched-chain fatty acids cannot be directly oxidized by mitochondrial enzymes; they undergo initial chain-shortening in peroxisomes.
• Acyl-CoA Oxidase (ACOX) is the rate-limiting first enzyme in peroxisomal $\beta$-oxidation.
• It catalyzes the desaturation of fatty acyl-CoA to trans-2-enoyl-CoA, transferring electrons directly to molecular oxygen ($O_2$) to generate hydrogen peroxide ($H_2O_2$), which is subsequently degraded by catalase.
• nalysis:
• (Peroxisome): Correct.
• (Mitochondria): The first enzyme in mitochondrial $\beta$-oxidation is acyl-CoA dehydrogenase, which transfers electrons to FAD/ETC, not oxygen.

Correct option: (4) Peroxisome