What is the area of the portion of the circle above created by arc ACB

I'm sorry that I am not able to post a diagram with my explanation but I hope my explanation can help you understand. And yes please do not feel seeing my detailed explanation that its a very long answer, it took me less than 2 mins and this is just to help you understand clearly

What are we given? Length of arc and radius of circle
What do we need? Area of the region between arc ACB and chord AB

Imagine the center of the circle O; A and B are points on the circle so OA and OB are both radius of the circle. Draw both these radius, will help you visualize the problem better
Once you draw both these radius, you can see that there is a triangle forming OAB and the area that we need = Area of Sector ACB - Area of Triangle OAB
Now that we have a clear solution path, let us use the information we have to get more information (we need to find central angle to find area of sector and then try and find the area of the triangle)

Length of arc = 2π
2πr * (Central angle/360) = 2π
2π(6) * (CI/360) = 2π
CI = 60

So CI or Central Angle is 60 and this is also 1 of the angle of Triangle OAB and the other 2 sides of the triangle are equal because they are radii of the circle so angles opposite to these sides will be equal, so
2A + 60 (the central angle) = 180 => A = 60
So all angles of triangle OAB are 60 degrees which means its an equilateral triangle and area for an equilateral triangle = Sqrt(3) * side^2 / 4 = 9 * sqrt(3) (because side = 6)

Area of sector = πr^2 * CI/360 = π 6^2 * 60/360 = 6π

Required area = Sector Area - Triangle Area = 6π - 9*sqrt(3) - E