I am going to assume you mean a regular hexagon.
Since it is regular, the hexagon can be broken down into 6 equal triangles. It is like cutting up a hexagonal cake, so each slice would have an angle of 360/6 degrees, so 60 degrees. You are told the radius is 6, so you now have a triangle where you know 2 sides (both 6) and the angle between them (60 deg). Hmm what sort of triangle would this be I wonder? Can you guess the answer yet? Now use the cosine rule to work out the opposite edge to the angle, which gives the length of one side of the hexagon. Now multiply it by 6 and you have your circumference.
Hint: the answer is 36 for the circumference of the hexagon, now you can do the working.
Edit: (just re-read your post and you might only be after the length of one side - in which case you dont multiply by 6 and the answer is 6)
For the second part, the same applies, split it into 6 triangles as before. Now find the area of the aforementioned triangle (cut the triangle in half and use pythag to find the height, which should be sqrt(27), then do 0.5*base*height). Now multiply it by 12 (as you cut it in half) and you have the area.
hint: the answer is 18*sqrt(27), now do the working.
So the main idea is to cut the hexagon into 6 equal triangles then calculate on that. I'll leave the other two to you for know, let me know if you need any more help on them.