A double hexagonal chain is a hexagonal system constructed by successive triple-edge fusions of naphthalenes. Oz and Cangul computed the Merrifield-Simmons index of the double hexagonal chain by utilizing Merrifield-Simmons vector defined at a path of double hexagonal chain. In this paper, inspired by Oz and Cangul's idea, by applying the perfect matching vector and maximal matching vector at a path of double hexagonal chain, we obtain the numbers of perfect matchings and maximal matchings of a double hexagonal chain with \( n \) naphthalenes.