For a regular polygon, the rotation about its center that keeps the polygon unchanged is:
![(360)/(n)\text{ degrees rotation}](https://img.qammunity.org/2023/formulas/mathematics/college/nt43my8yu56o3k8xdn6aygt3l35owpnc9k.png)
where n is the number of sides of the polygon.
In this case, n=6, therefore, a 360/6=60° clockwise rotation about the center of the hexagon would result ina hexagon with the same vertices.