Step 1 Divide a circle into twelve equal sections. (You can download and print a template here)
tegel07-01a

Step 2 Draw a hexagon in the circle.
 
 

tegel07-01b

Step 3 Draw four lines that connect to the intersections indicated with red circles. It helps to consider the lines as two opposing V-shapes.
tegel07-02

Step 4 Draw another two opposing V-shapes, as indicated. Make sure the point of V does not touch the circle but the hexagon,tegel07-03

Step 5 Draw another two opposing V-shapes, as indicated.

Step 6 All the construction lines have now been drawn. Take a different colour pen or pencil and draw the red lines, tracing parts of lines you have drawn in the previous steps.

Step 7 Draw the remaining red lines, as indicated.

Step 8 All the lines have been drawn, your pattern is complete.
tegel07-07

Step 9 Your pattern without the construction lines.

Step 10 Now you can tessellate your pattern in a grid of hexagons to make a bigger composition. If you’re working in a group, tessellate all the patterns together.