Explanation

(c)
$\sin{12{^\circ}\sin{48{^\circ}\sin{54{^\circ}}}}$
$= \frac{1}{2}\left\lbrack \cos{36{^\circ} - \cos{60{^\circ}}} \right\rbrack\cos{36{^\circ}}$
$= \frac{1}{2}\left\lbrack \frac{\sqrt{5} + 1}{4} - \frac{1}{2} \right\rbrack\left\lbrack \frac{\sqrt{5} + 1}{4} \right\rbrack = \frac{1}{8}$