Clear[f]
f[x_,y_] = 18-(x^2+y^2);
Plot3D[f[x,y], {x,-3,3},{y,-3,3}]

Clear[blist2];
blist2 = Table[Plot3D[a, {x,-3,3},{y,-3,3},Mesh->False,MeshShading->False,PlotStyle->{Blue},PlotRange->{0,20}]  , {a,1,13,3}     ]

Table[
Show[{blist2[[i]],Plot3D[f[x,y], {x,-3,3},{y,-3,3},Mesh->False]},PlotRange->{0,19}],  {i,1, Length[blist2]}  ]

Clear[blist3];
blist3=Table[   
 ContourPlot[f[x,y]==a, {x,-3,3},{y,-3,3},ContourStyle->{Thick,Blue,Dashing[{.03}]}, Contours->1],          {a,1,13,3}   ];
Clear[conPlotf];
conPlotf = ContourPlot[f[x,y], {x,-3,3},{y,-3,3}, Contours->7,ContourShading->False] ;

Table[   Show[{  blist3[[i]],  conPlotf  }],  {i,1, Length[blist2]}     ]

Table[
{Show[{blist2[[i]],Plot3D[f[x,y], {x,-3,3},{y,-3,3},Mesh->False]},PlotRange->{0,19}],
Show[{  blist3[[i]],  conPlotf  }]},  {i,1, Length[blist2]}  ]

Manipulate[
{Show[{blist2[[i]],Plot3D[f[x,y], {x,-3,3},{y,-3,3},Mesh->False]},PlotRange->{0,19}],
Show[{  blist3[[i]],  conPlotf  }]},  {i,1, Length[blist2],1}  ]