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?

To determine the number of dots on each face of the dice after the given rotations, we need to consider the orientation of the dice before and after the rotations. Let's break down the steps to find the solution:

Step 1: Initial Position
The initial position of the dice is described as follows:
- Top: 3
- Right Back: 6
- Right Front: 2
- Bottom: 4
- Left Front: 1
- Left Back: 5

Step 2: Rotating +180 degrees about the z-axis
When a dice is rotated 180 degrees about the z-axis, the top and bottom faces remain the same, the front face becomes the back face, and the left and right faces switch places. Applying this rotation to our initial position, we get the following configuration:
- Top: 3
- Right Back: 5
- Right Front: 1
- Bottom: 4
- Left Front: 2
- Left Back: 6

Step 3: Rotating +90 degrees about the x-axis
When a dice is rotated 90 degrees about the x-axis, the top face becomes the front face, the front face becomes the bottom face, the bottom face becomes the back face, and the back face becomes the top face. The left and right faces do not change. Applying this rotation to the previous configuration, we get the following final configuration:
- Top: 4
- Right Back: 5
- Right Front: 1
- Bottom: 2
- Left Front: 6
- Left Back: 3

So, the final configuration of the dice after the given rotations is:
- Top: 4
- Right Back: 5
- Right Front: 1
- Bottom: 2
- Left Front: 6
- Left Back: 3

Therefore, each face of the dice has the following number of dots after the rotations:
- Top: 4 dots
- Right Back: 5 dots
- Right Front: 1 dot
- Bottom: 2 dots
- Left Front: 6 dots
- Left Back: 3 dots