Three different positions of the same dice are given. Find the number on the face opposite to the face showing ‘6’.

The correct answer is 2.

Step-by-Step Explanation:

Step 1: Observe the given positions of the dice
In all three positions of the dice shown in the image:
- First position: The top face shows 4, the left face shows 3, and the right face shows 2.
- Second position: The top face shows 4, the left face shows 2, and the right face shows 5.
- Third position: The top face shows 4, the left face shows 5, and the right face shows 6.

Step 2: Analyze the adjacent faces of 4
Since the face showing 4 is at the top in all three views, the four surrounding faces adjacent to 4 are 3, 2, 5, and 6.

Step 3: Determine opposite pairs
By tracing the sequence of adjacent faces around face 4:
- 2 is adjacent to 3 and 5.
- 5 is adjacent to 2 and 6.
- 6 is adjacent to 5 and 3.
- 3 is adjacent to 6 and 2.

On a 6-sided dice, faces that are opposite each other cannot be adjacent. In the circular arrangement of four adjacent faces (3, 2, 5, 6):
- The face opposite to 3 is 5.
- The face opposite to 6 is 2.
- The face opposite to 4 is the remaining face, 1.

$\text{Opposite face to 6}=2$

Therefore, the number on the face opposite to the face showing ‘6’ is 2.