From the theorem of parallel axis, the moment of inertia $I$ is equal to
$I=I_{CM}+M{a}^2$
where $I_{CM}$ moment of inertia is about centre of mass and $a$ the distance of axis from centre.
$\therefore$ $I=M{K}^2+M\times {\left(6\right)}^2$
$M{K}_1^2=M{K}^2+36M$
$\Rightarrow$ $K_1^2=K^2+36$
$\Rightarrow$ ${\left(10\right)}^2=K^2+36$
$\Rightarrow$ $K^2=100-36=64$
$\Rightarrow$ $K=8$ cm