Explanation :
For elastic collision
$m_1u_1+m_2u_2=m_1v_1+m_2v_2\;\;\_\_(1)moment\;conservation$
$(1\times12)+(2\times0)=(1\cdot v_1)+(2\cdot v_2)$
$12+0=v_1+2v_2\;\;\_\_(2)$
$1/2\;m_1u_1^2+1/2\;m_2u_2^2=1/2\;m_1v_1^2+1/2\;m_2v_2^2\;\_\_(3)$
$(1/2\cdot1\cdot12^2)+(1/2\cdot2\cdot0^2)=(1/2\cdot1\cdot v_1^2)+(1/2\cdot2\cdot v_2^2)$
$144+0=v_1^2+2v_2^2\;\;\_\_(4)$
$From\;(2)\;\;v_1=12-2v_2$
$144=(12-2v_2)^2+2v_2^2$
$144=144-48v_2+4v_2+2v_2^2$
$6v_2^2-48v_2=0$
$6v_2(v_2-8)=0$
$\therefore\;v_2=8\;m/sec$