$\begin{array}{1 1} (a)\;0.06\;m & \quad (b)\;0.04\;m \\ (c)\;0.02\;m & \quad (d)\;none\;of\;these \end{array}$

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At maximum compression velocity of both bodies are same and equal to velocity of centre of mass

By momentum conservation

$m_1V_1+m_2V_2=(m_1+m_2)V$

$V= \large\frac{12+12}{6}$$=4\;m/s$

By energy conservation:

$\large\frac{1}{2}$$m_1v_{1}^2+\large\frac{1}{2}$$m_2v_{2}^2=\large\frac{1}{2} $$(m_1+m_2)V^2+\large\frac{1}{2} $$k x^2$

$\frac{1}{2}kx^2=\large\frac{1}{2}. $$2 \times 36 +\large\frac{1}{2} $$. 4 \times 9-\large\frac{1}{2} $$(6) 16$

$\qquad=54 - 48$

$x^2=\large\frac{12}{k}$

$x=\sqrt {\large\frac{12}{30000}}$

$\qquad= \sqrt {\large\frac{1}{2500}}$

$\qquad=\large\frac{1}{50}$

$\qquad = 0.02\;m$

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