Six-dimensional movable antenna (6DMA) has been widely studied for capacity enhancement, but its potential for physical layer security (PLS) remains largely unexplored. By adjusting both three-dimensional (3D) positions and 3D rotations of distributed antenna surfaces, 6DMA can increase spatial degrees of freedom (DoFs). The extra DoFs enable dynamic shaping of legitimate channels and suppresses eavesdropping channels, thereby offering unique advantages in enhancing secrecy performance. Motivated by this, this letter proposes a novel 6DMA-assisted secure wireless communication system, where the base station (BS) is equipped with 6DMA to enhance secrecy performance. Specifically, to simultaneously serve multiple legitimate users and counter cooperative interception by multiple eavesdroppers (Eves), we formulate a sum secrecy rate (SSR) maximization problem by jointly optimizing the transmit and artificial noise (AN) beamformers, as well as the 3D positions and 3D rotations of antenna surfaces. To solve this non-convex problem, we propose an alternating optimization (AO) algorithm that decomposes the original problem into two subproblems and solves them iteratively to obtain a high-quality suboptimal solution. Simulation results demonstrate the superior secrecy performance over partially movable and conventional fixed-position antenna systems.