This paper studies the distributed optimization problem for discrete-time general second-order multi-agent systems (MASs). In this problem, each agent is subject to individual set constraints. The agents collaborate to find the optimal solution of a global objective function, which is the sum of local objective functions, within the intersection of their constraint sets. A projection-based distributed event-triggered algorithm is proposed for general second-order systems, enabling agents to achieve consensus and gradually converge to the optimal solution while effectively reducing communication costs.