Final answer:
The coin that replaced the silver half-dime in 1866 was the Nickel (A).
Step-by-step explanation:
The coin that Congress authorized to replace the silver half-dime in 1866 was the Nickel (A). Congress passed the Coinage Act in 1835, which shifted towards a hard money policy. This policy replaced paper currency with gold coins in commercial transactions. The nickel coin was introduced as part of this shift.