A rectangle of side 8cm\times 6cm and a rhombus

Area of rectangle:
$8 \times 6 = 48$

Area of rhombus:
$8^2 \times \sin 60^\circ = 64 \times \frac{\sqrt{3}}{2} = 32\sqrt{3}$

Now, ratio (rectangle : rhombus):
$48 : 32\sqrt{3}$

Simplify:
Divide by 16 → $3 : 2\sqrt{3}$

Rationalize:
$= \frac{3}{2\sqrt{3}} = \frac{3}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{6} = \frac{\sqrt{3}}{2}$

So,
$= \sqrt{3} : 2$

Answer: $\sqrt{3} : 2$