Plotting the Tangent Plane
First, solve the tangent plane equation for z as a function of x and y. I'll call this "z_pl".
> z_pl:=solve(-(x+2)+2*(y-1)-2/3*(z+3)=0,z);
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This plane can now be plotted in parametric form, where x and y are the parameters.
> plot3d([x,y,z_pl],x=-3..1,y=0..2);
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