We start with a line segment AF.
This will become one side of the hexagon.
Because we are constructing a regular hexagon, the other five sides will have this length also. 

1. Set the compasses' point on A, and set its width to F. the compasses must
remain at this width for the remainder of the construction. 

2. From points A and F, draw two arcs so that they intersect. Mark this as point O.
This is the center of the hexagon's circumcircle. 

3. Move the compasses to O and draw a circle.
This is the hexagon's circumcircle  the circle that passes through all six vertices


4. Move the compasses on to A and draw an arc across the circle.
This is the next vertex of the hexagon. 

5. Move the compasses to this arc and draw an arc across the circle to create the next vertex. 

6. Continue in this way until you have all six vertices.
(Four new ones plus the points A and F you started with.) 

7. Draw a line between each successive pairs of vertices. 

8. Done. These lines form a regular hexagon where each side is equal in length to AF. 
