In this talk, I will show that every point in the hyperbolic 3-space is moved at a distance at least $\frac{1}{2}\log(12.3^{k−1}-3)$ by one of the isometries of length at most $k\geq2$ in a 2-generator Klenian group $\Gamma$ which is torsion-free, not co-compact and contains no parabolic. Also I will propose some lower bounds for the maximum of hyperbolic displacements given by symmetric subsets of isometries in purely loxodromic finitely generated free Kleinian groups.