A particle doing simple harmonic motion, amplitude = 4 cm, time period = 12 sec.  The ratio between time taken by it in going from its mean position to 2 cm and from 2 cm to extreme position is

$\omega =\frac{2\pi }{T}=\frac{2\pi }{12}=\frac{\pi }{6}\frac{rad}{\sec }$

(For y = 2 cm)

 2 = $4\left(\sin \frac{\pi }{6}{t}_1\right)$

By solving, $t_1=1$sec 

(For y = 4 cm), $t_2=3$sec

So, time taken by particle in going from 2 cm to extreme position is $t_2-t_1=2$sec.  

Hence, required ratio will be $\frac{1}{2}$.