In a region the potential is represented by $V\left(x, y, z\right)=6x-8xy-8y+6yz,$ where $V$ is in volts and $x, y, z,$ are in meters. The electric force experienced by a charge of $2$ coulombs situated at point $\left(1, 1, 1\right)$ is:

Potential in the space varies as $V_{\left(x, y, z\right)}=6x-8xy-8y+6yz$.

Electric field is given by,
$E_x=-\frac{\partial V}{\partial x}=-6+8y$
$E_y=-\frac{\partial V}{\partial y}=8x+8-6z$
$E_z=-\frac{\partial V}{\partial z}=-6y$
$\overrightarrow{E}=\left(-6+8y\right) \hat{i}+\left(8x+8-6z\right)\hat{j}-6y \hat{k}$

Putting the value of the position we get,
${\overrightarrow{E}}_{\left(1, 1, 1\right)}=2\widehat{i}+10\widehat{j}-6\widehat{k}$

Magnitude is given by,
$\left|\overrightarrow{E}\right|=2\sqrt{35} N{C}^{-1}$

Force on the charge is given by,
$F=qE=2\times 2\sqrt{35}=4\sqrt{35} N$