Spiking Neural Networks (SNNs) offer a biologically inspired foundation for low-power, event-driven intelligence, yet their direct on-chip supervised training remains a key hardware challenge. This paper presents a multiplication-free, spike-time-based learning algorithm specifically designed for efficient FPGA realization. The proposed approach eliminates floating-point arithmetic and explicit gradient storage, enabling a fully event-driven, digital training pipeline. Implemented on a Xilinx Artix-7 FPGA, the architecture achieves high operating speed and minimal resource usage while maintaining competitive accuracy. These results demonstrate that the learning algorithm effectively maps onto reconfigurable hardware, achieving both computational and energy efficiency. Software simulations further validate scalability, with 96.5\% and 84.8\% accuracy on MNIST and Fashion-MNIST. With its spike-driven and multiplier-free operation, the proposed framework delivers a practical and scalable hardware solution for real-time, on-chip SNN learning in edge environments.