The random experiment is "Rolling two dice"

Let $S$ be the sample space, $n\left(S\right)=6^2=36$

Let $E$ be the event of getting even numbers on them

$E=\left\{\left(2,2\right),\left(2,4\right),\left(2,6\right),\left(4,2\right),\left(4,4\right),\left(4,6\right),\left(6,2\right),\left(6,4\right),\left(6,6\right)\right\}$

There are 9 favourable cases for the event $E$

Hence, $n\left(E\right)=9$

Therefore, the required probability is $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{9}{36}=\boxed{\frac{1}{4}}$