Given data

• Mass of block: $m = 0.5\,\text{kg}$
• Initial speed: $u = 12\,\text{m s}^{-1}$
• Final speed when compressed by $x=30\,\text{cm}=0.30\,\text{m}$: $v = \dfrac{12}{2}=6\,\text{m s}^{-1}$

Apply work-energy theorem

As the block compresses the spring, part of its kinetic energy is converted into spring potential energy.

So, $\frac12 m u^2 = \frac12 m v^2 + \frac12 k x^2$

Rearranging, $\frac12 k x^2 = \frac12 m (u^2-v^2)$

Substitute values

$\frac12 k (0.30)^2 = \frac12 (0.5)(12^2-6^2)$

$\frac12 k (0.09) = 0.25(144-36)$

$0.045k = 0.25(108)$

$0.045k = 27$

Solve for $k$

$k = \frac{27}{0.045} = 600\,\text{N m}^{-1}$

Final answer

$\boxed{600}$