How do I lower my body fat without changing my weight (up or down)?

Not easy . But have heart, if you are very regimented about your diet and exercise habits it's possible to lose body fat and gain muscle mass so tgat your overall weight stays the same.
Not possible. . If you only loose body fat you will loose weight. If you do it by exercise, you will loose fat but replace it with muscle that weighs more. You will be more toned & look much better & also feel better & self image will improve. .