Six-dimensional movable antenna (6DMA) is an emerging technology that is able to fully exploit the spatial variation of wireless channels by controlling the 3D positions and 3D rotations of distributed antennas/antenna surfaces at the transmitter/receiver. In this letter, we apply 6DMA at the base station (BS) to enhance its wireless sensing performance over a given set of regions. To this end, we first divide each region into a number of equal-size subregions and select one typical target location within each subregion. Then, we derive an expression for the Cramer-Rao bound (CRB) for estimating the directions of arrival (DoAs) from these typical target locations in all regions, which sheds light on the sensing performance of 6DMA enhanced systems in terms of a power gain and a geometric gain. Next, we minimize the CRB for DoA estimation via jointly optimizing the positions and rotations of all 6DMAs at the BS, subject to practical movement constraints, and propose an efficient algorithm to solve the resulting non-convex optimization problem sub-optimally. Finally, simulation results demonstrate the significant improvement in DoA estimation accuracy achieved by the proposed 6DMA sensing scheme as compared to various benchmark schemes, for both isotropic and directive antenna radiation patterns.