Step-by-step Solution:

Multiply and divide by \( \sin 72 \), we get: \[ \frac{\sin 12 \sin 48 \sin 72 \sin 54}{\sin 72} \] \[ = \frac{\sin 36 \sin 54}{4 \sin 72} \quad \text{(using } \sin \theta \sin (60 - \theta) \sin (60 + \theta) = \frac{\sin 3\theta}{4} \text{)} \] \[ = \frac{2 \sin 36 \sin 54}{8 \sin 72} = \frac{2 \sin 36 \cos 36}{8 \sin 72} = \frac{1}{8} \]