problem

The  circumference of  the base  of each cone will be the arc length of one of the sectors  =

2 pi (6)  / 3  =  4 pi  inches

So....the radius, r, of each cone (in inches) is given  by :

4pi  =  2 pi * r

4  = 2r

2  = r   

And the slant height of each cone  is the radius of the original circle

And the radius of the cone and its height will form two legs of a right triangle with a hypotenuse of 6 inches  (the slant height)

So...using the Pythagorean Theorem, the cone height, h, is given by :

h  = √[ slant height^2  - radius^2 ]  =  √ [ 6^2  - 2^2 ] = √32  =  4√2  inches