I assume you mean the paraboloid \(x=6y^2+6z^2\). Denote the space between this surface and the plane \(x=6\) by the symbol \(D\).
The volume is then
\(\displaystyle\iiint_D\mathrm dV=\int_{-1}^1\int_{-1}^1\int_{6y^2+6z^2}^6\mathrm dx\,\mathrm dy\,\mathrm dz=8\)
