\[\sin{24{^\circ}} \cdot \sin{6{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \cos{18{^\circ}} - \cos{30{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \cos{18{^\circ}} - \frac{\sqrt{3}}{2} \right) =\]
\[= \frac{1}{2}\cos{18{^\circ}} - \frac{\sqrt{3}}{4}\]