Question: Use Lagrange multipliers to find the indicated extrema

\[\begin{aligned} & \text{Maximize}\,\,\,\,\,f\left( x,y,z \right)={{x}^{2}}+{{y}^{2}}+{{z}^{2}} \\ & \text{s}\text{.t}\text{.}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+2z=6 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y=12 \\ \end{aligned}\]