This study investigates the link between cigarette smoke, specifically benzo(a)pyrene (BaP), and cerebral palsy, focusing on BaP’s neurotoxicity. It also examines the neuroprotective potential of hesperidin, a citrus-derived compound, by assessing its binding affinity with the β4 subunit of Adapter Protein Complex 4 (AP-4). Molecular docking analyses using Discovery Studio and PyRx were performed with the β4 subunit of AP-4 as the protein and benzo(a)pyrene and hesperidin as ligands. The results showed that hesperidin had a higher binding affinity (-7.2 kcal mol-1) compared to BaP (-6.5 kcal mol-1), establishing multiple interactions, including van der Waals, hydrogen, and pi-alkyl bonds. Key receptor residues for hesperidin binding were identified. These findings highlight hesperidin’s potential neuroprotective role, suggesting it may help to prevent BaP-induced neurotoxicity in cerebral palsy. The study emphasizes the promise of hesperidin, encouraging further in vivo and clinical investigations.