STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = \frac{ 3 }{ 4 } $$
STEP 2: find diagonal $ d $
To find diagonal $ d $ use formula:
$$ d = 2 \cdot a $$After substituting $ a = \frac{ 3 }{ 4 } $ we have:
$$ d = 2 \cdot \frac{ 3 }{ 4 } $$ $$ d = \frac{ 3 }{ 2 } $$