Unpolarized light of intensity I_0 passes through four polaroids...

When unpolarized light of intensity $I_0$ passes through the first polaroid, its intensity is halved:
$I_1 = \dfrac{I_0}{2}$

The light then passes through the second polaroid, whose axis is at $30^{\circ}$ to the first. According to Malus's Law:
$I_2 = I_1 \cos^2(30^{\circ}) = \dfrac{I_0}{2} \times \left(\dfrac{\sqrt{3}}{2}\right)^2 = \dfrac{I_0}{2} \times \dfrac{3}{4}$

The third polaroid is at $30^{\circ}$ to the second:
$I_3 = I_2 \cos^2(30^{\circ}) = \left(\dfrac{I_0}{2} \times \dfrac{3}{4}\right) \times \dfrac{3}{4} = \dfrac{I_0}{2} \times \left(\dfrac{3}{4}\right)^2$

The fourth polaroid is at $30^{\circ}$ to the third:
$I_4 = I_3 \cos^2(30^{\circ}) = \dfrac{I_0}{2} \times \left(\dfrac{3}{4}\right)^2 \times \dfrac{3}{4} = \dfrac{I_0}{2} \times \left(\dfrac{3}{4}\right)^3$

Calculating the final value:
$I_4 = \dfrac{I_0}{2} \times \dfrac{27}{64} = \dfrac{27 I_0}{128}$

Answer: $\dfrac{27 I_0}{128}$