Find a point on the surface $f=2 x^{2}-y^{2}-4 x+z^{2}=10$ where its tangent plane is parallel to the plane $P=2 y+4 z=3$

Question

Find a point on the surface $f=2 x^{2}-y^{2}-4 x+z^{2}=10$ where its tangent plane is parallel to the plane $P=2 y+4 z=3$

I did the gradient of f

$[4x-4,-2y,2z]$

and gradient of P

$[0,2,4]$

and then I did

$4x-4=0\\-2y=2t\\2z=4t$

and Im stuck here $x=1, y=-t, z=2t$

and then I put that values on $f$ and resolve for $t$

and I get $t=-2,2$

and from here I don't know what to do, or Im doing bad things?