A particle starting from rest with uniform acceleration travels a distance x in first 2 second and a distance y in next 2 second, then

Here u=0 

For t = 2s, s=x 

Using $\mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2$

$\mathrm{x}=\frac{1}{2}\mathrm{a}\times 2^2=2\mathrm{a}$
Next 2 s, the particle travels y,

$\Rightarrow \mathrm{t}=(2+2)\mathrm{s}=4\mathrm{s}$

$\hspace{0.17em}\hspace{0.17em}\mathrm{s}=\mathrm{x}+\mathrm{y}$

$\Rightarrow \left(\mathrm{x}+\mathrm{y}\right)=\frac{1}{2}\mathrm{a}{\left(4\right)}^2=8\mathrm{a}$
$\Rightarrow \left(\mathrm{x}+\mathrm{y}\right)-\mathrm{x}=8\mathrm{a}-2\mathrm{a}=6\mathrm{a}$   or $\mathrm{y}=6\mathrm{a}=3\left(2\mathrm{a}\right)\Rightarrow \mathrm{y}=3\mathrm{x}$