Hexagonal diamond (HD) was reported 60 years ago and has attracted extensive attention owing to its ultrahigh theoretical hardness, 58% superior to its cubic counterpart. However, to date, synthesizing pure HD under high-pressure and high-temperature (HPHT) remains unsuccessful due to the limitations of understanding the formation mechanism. In this work, employing a systematic molecular dynamics simulation, we directly observe the graphite-to-HD transition in a nucleation-growth mechanism. Specifically, HD is formed under quasi-uniaxial compression with higher stress along the [001] direction of graphite and mild-temperature conditions for the scarce sliding of the graphite basal plane, while cubic diamond (CD) is formed when the AB-layer stacking structure of graphite is destroyed and/or freely sliding under a higher temperature. Our theoretic work is well confirmed by the controlled HPHT experiment, where HD was successfully synthesized under quasi-uniaxial conditions with high stress in the [001]g direction, while CD was synthesized when AB-layer stacking was disturbed by higher compressive stress parallel to the basal sheets. Our work not only clarifies the pressure-temperature-controlled mechanisms of graphite-to-diamond transitions but also guides a novel approach to synthesize HD by maintaining the graphite basal plane (001) in an AB-stacking configuration and precisely controlling the basal layer sliding.