The point (–1, 4, –2) lie in the octant

The position of the point in which octant it lies depends on the sign of coordiantes 

In the given point $\left(-1,4,-2\right)$, only $y-$coordinate is positive, remaining two coordinates are negative

hence, the octant in which the point $\left(-1,4,-2\right)$ lies is $\boxed{\mathbf{O}\mathbf{X}\mathbf{\text{'}}\mathbf{Y}\mathbf{Z}\mathbf{\text{'}}}$