Body A of mass 4 m moving with speed u collides with another body B of mass 2 m at rest. The collision is…

$4mu+0=4m{v}_1+2m{v}_2$
$\Rightarrow 2u=2v_1+v_2 \dots \left(\mathrm{A}\right)$
For elastic collision, 
$e=1$
$\Rightarrow u=v_2-v_1 \dots \left(\mathrm{B}\right)$

From $\left(\mathrm{A}\right)\mathrm{ }$ and $\left(\mathrm{B}\right)$, 
$4u=3v_2\Rightarrow v_2=\frac{4}{3}u$
and $v_1=\frac{u}{3}$
Fraction of energy lost by $\left(\mathrm{A}\right)$, 
$=\frac{\frac{1}{2}4m{u}^2 - \frac{1}{2}4m{v}_1^2}{\frac{1}{2}4m{u}^2}$
$=\frac{u^2 - \frac{u^2}{9}}{u^2}=\frac{8}{9}$