The time taken by a particle executing SHM of period T to move from the extreme  position to half the maximum displacement is

For a particle executing simple harmonic motion starting from extreme position,  the equation for displacement is  y=Acosωt   i.e., A2=Acos2πTt . On simplifying this we get  12=cos2πTt. To satisfy this condition, π3=2πTt , i.e.  T6=t