levelFunction[x_,y_,z_]:=x y z;
levelPlaneTangent[x_,y_,z_]:=x+4y+2z;
levelConstant=8;
planeNormal=12;
fixedPoint={4,1,2};

Show[ContourPlot3D[levelFunction[x,y,z]==levelConstant,{x,-4,4},{y,-4,4},{z,-4,4}],
ContourPlot3D[levelPlaneTangent[x,y,z]==planeNormal,{x,-4,4},{y,-4,4},{z,-4,4},ContourStyle->Directive[Black]],
Graphics3D[{Red,PointSize[0.05],Point[fixedPoint]}]]

N.B. The red dot indicates the location of the fixed point.

SetOptions[SelectedNotebook[],PrintingStyleEnvironment->"Printout",ShowSyntaxStyles->True]