posted by PLEASE HELP .
If a dice has 3 on the top, right back 6, right front 2, bottom 4, left front 1, left back 5 and is rotated by +180 about the z axis and +90 about the x axis, how many dots does each face have after the rotation?
You talk about front, bottom, left
then you mention x axis, z axis.
Where are the axis?
the z axis is top/ bottom, the x/y axis is right/ left
180° about z takes (x,y,z) -> (-x,-y,z)
90° about x takes (x,y,z) -> (x,z,-y)
so, your two rotations take (x,y,z) -> (-x,z,y)
So, figure where the spots start out, and apply the rotations.