Explanation:

Charles Babbage designed two significant mechanical computing devices: the Difference Engine and the Analytical Engine. His (c) 'Calculator' refers to the Difference Engine, which was his first major design (starting in 1822) intended to automate the calculation of polynomial functions for mathematical tables. It was a specialized mechanical calculator. The Analytical Engine, conceived later, was a more general-purpose mechanical computer. Option (a) Palmtop is a modern, very small portable computer. Option (b) Processor is a general term for a component that carries out instructions. Option (d) Punchcard machine is more associated with Herman Hollerith's tabulating machines, although Babbage's Analytical Engine was designed to use punch cards for input. Therefore, 'Calculator' ($ \text{c} $) best describes his first mechanical computing device, the Difference Engine.