\(\left(\dfrac{1}{68}+\dfrac{1}{968}-\dfrac{1}{1969}\right)\left(\dfrac{1}{23}-\dfrac{1}{6}-\dfrac{1}{6}\right)\)
\(=\dfrac{44865}{2945624}\cdot\left(-\dfrac{20}{69}\right)\)
\(=-\dfrac{14955}{736406}\cdot\dfrac{5}{23}\)
\(=-\dfrac{74775}{16937338}\)