$\phi=4xz^3-3x^2y^2z$ $\Delta\phi=i\dfrac{\partial\phi}{\partial x}+j\dfrac{\partial\phi}{\partial y}+k\dfrac{\partial\phi}{\partial x}$ $\Delta\phi=i\dfrac{\partial(4xz^3-3x^2y^2z)}{\partial x}+j\dfrac{\partial(4xz^3-3x^2y^2z)}{\partial y}+k\dfrac{\partial(4xz^3-3x^2y^2z)}{\partial x}$ $\Delta\phi=i(4z^3-6xy^2z)+j(-6yx^2z)+k(12z^2x-3x^2y^2)$ =$8i-24j-84k$ at(2,-1,2) Directional derivative in the direction of($(2i+3j+6k)$ multiplication of the dot(.)product  $(ai+bj+ck).(di+ej+fk)=(a\times d)+(b\times e)+(c\times k)$ $(2i+3j+6k).$$8i-24j-84k=(2\times8)+(3\times-24)+(6\times-84)=-560$ =$(2i+3j+6k).\dfrac{(8i-24j-84k)}{\sqrt{4+4+1}}=\dfrac{-560}{3}$