This study focuses on synthesizing and optimizing a fly ash-based geopolymer modified with activated carbon to efficiently remove manganese from contaminated solutions within a permeable reactive barrier. Using the RSM-BBD strategy, the synthesis process was optimized, resulting in influential parameters set at 40% activated carbon with fly ash as a precursor, 12 M NaOH concentration, 2.5 Na2SiO3/NaOH ratio, 55 degrees C curing temperature, 14 h curing time, 30% solid content, and 37 kHz sonication. Characterization via FESEM revealed the sorbent's high porosity, crystalline nature, and heterogeneous surface with a wide size distribution. The potential of the synthesized geopolymer sorbent to eliminate Mn2+ from synthetic wastewater was further assessed using the RSM-CCD approach. Results showed complete removal of Mn2+ ions at a solution pH of approximately 2.3, adsorbent dosage of 0.2 g, pollutant solution volume of 20 ml, pollutant concentration of 500 ppm, stirring rate of around 300 rpm, and contact time of approximately 60 min. Additionally, sorption kinetics, isotherms, thermodynamics, and possible adsorption mechanisms were scrutinized. Kinetic data revealed that the phenomenological internal mass transfer (IMT) model provided the best fit, with internal diffusion as the rate-controlling mechanism. Isotherm analysis confirmed multilayered and homogeneous interactions between the adsorbent and adsorbate, with a physical adsorption type. Thermodynamic results indicated feasible, spontaneous, and endothermic sorption.