We present an interactive physics-based motion synthesis technique for creating hand manipulation across a wide variety of tasks, objects, user interventions, and stylistic preferences. Given an object being manipulated, a single pose specifying the desired initial contact, and the kinematic goals of the manipulation, our algorithm automatically generates hand-object manipulation that is responsive to unscripted external disturbances. Our algorithm simulates the dynamic coupling between a passive dynamic system and an active dynamic system by formulating a sequence of constrained optimizations. This formulation allows the user to synthesize a manipulation task by describing simple, keyframe-like kinematic goals in the domain of object configuration. The algorithm will automatically produce the hand motion that achieves the kinematic goals via coupled dynamic equations of motion.