Arrange the points : A(1, 2, 3); B(–1, 2, –3); C(–1, –2, –3) and D(1, –2, –3) in the increasing order of their octant numbers :

The octant where the point lies depends on the signs of coordinates of point

$A\left(1,2,3\right)$, all are posiitve, so that the octant that A lies is $OXYZ$, this is first octant

$B\left(-1,2,-3\right)$ , both $x,z$coordinates are negative and $y$ coordinate is positive. so it lies in $OX\text{'}YZ\text{'}$, it is 6th Octant.

$C\left(-1,-2,-3\right)$ , all are negative, then the octant in which the point lies is $OX\text{'}Y\text{'}Z\text{'}$, it 7th octant

$D\left(1,-2,-3\right)$ both $y,z$ are negativve, and x is posiitive, hence the octant in which the point lies is $OXY\text{'}Z\text{'}$, it is 8th octant

Hence, the increasing order of the octants in which the points lies is $A,B,C,D$