Answer
The maximum compression of the spring is 0.085 meters.
Work Step by Step
The kinetic energy of the box will be equal to the elastic potential energy stored in the spring.
$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$
$x^2 = \frac{mv^2}{k}$
$x = v~\sqrt{\frac{m}{k}}$
$x = (3.0~m/s)~\sqrt{\frac{6.0~kg}{7500~N/m}}$
$x = 0.085~m$
The maximum compression of the spring is 0.085 meters.
