Answer:
Attachment 1
Take a compass and adjust it so that it is the width of line r.
Place the point of the compass on the left point of line r and draw a circle going through the right point of line r with radius r.
Attachment 2
Take a ruler, place it so it is against line r and extend the line r across the width of the circle (this is the diameter of the circle).
Attachment 3
Place the point of the compass on the right point of line r and draw a circle (blue circle).
Place the point of the compass on the left of the diameter and draw a circle (orange circle)
Attachment 4
The points of intersection of the 3 circles are the vertices of the hexagon.
Attachment 5
Join the points of intersection with line segments - this is your hexagon with sides equal to r.
(If necessary, erase the circles to show the hexagon only.)