#### Answer

AD =8 inches

#### Work Step by Step

Diagonal AD splits the hexagon into 2 isoceles trapezoids. Draw diagonals FB and EC to observe that AD equal the sum of BC and 2 short legs of 30 60 90 triangles. The legs are equal to one half of their correspond hypotenuses which would be 4/2=2.
AD=4+2+2
AD=8