Designing anthropomorphic robotic hands that balance functional dexterity with mechanical simplicity remains a significant challenge. Inspired by human hand synergies, this paper presents the SyLink Hand, an anthropomorphic dexterous hand that integrates biomechanical synergy principles with linkage-driven transmission mechanisms to achieve a high degree of anthropomorphism in appearance, kinematics, and functionality within a compact and cost-effective architecture. Biomechanical analysis of natural hand motions using motion capture gloves reveals strong kinematic correlations among hand joints, providing the basis for a simplified yet functional degree-of-freedom (DOF) configuration. Guided by these synergistic characteristics, optimized linkage mechanisms are employed to coordinate multiple joint motions and reproduce natural finger trajectories. A novel spherical four-bar linkage is further proposed to achieve decoupled flexion/extension (Flex/Ext) and abduction/adduction (Abd/Add) at the metacarpophalangeal joint within a compact form factor. The resulting prototype integrates 19 joints driven by 11 actuators, with a total mass of 520g and a manufacturing cost of approximately USD 400. Experimental evaluations demonstrate its human-like kinematic performance, high load-bearing capability, and versatile grasping and manipulation skills. These results validate that the synergy-inspired, linkage-based design effectively balances anthropomorphism, mechanical simplicity, and functional versatility, highlighting its potential for practical deployment in dexterity-demanding robotic applications.