Intelligence is as much a behavior as education is. You observe it by what people do and how they perform. There is no physical or neurological correlate of intelligence like height or brain size or white matter integrity which measures intelligence as well as observing performance does.
As for how education can be genetically mediated, there's many ways. Through intelligence (high genetic correlation/overlap), but also through personality traits, ADHD-proneness, and other mental and physical characteristics which are undoubtedly under genetic control.
As for how education can be genetically mediated, there's many ways. Through intelligence (high genetic correlation/overlap), but also through personality traits, ADHD-proneness, and other mental and physical characteristics which are undoubtedly under genetic control.