Explanation:

To find the unit digit of the given number, we need to find the remainder when the number is divided by 10. The unit digit is the remainder in this case.

Method 1: Using the cyclicity of the unit digits

- We know that the unit digit of any power of 2 repeats in a cycle of 4. The cycle is 2, 4, 8, 6.
- Therefore, to find the unit digit of 634262, we need to find the remainder when 634262 is divided by 4.
- 634262 ÷ 4 = 158565 with a remainder of 2.
- Since the remainder is 2, the unit digit of 634262 is the second digit in the cycle, which is 4.
- Similarly, to find the unit digit of 634263, we need to find the remainder when 634263 is divided by 4.
- 634263 ÷ 4 = 158565 with a remainder of 3.
- Since the remainder is 3, the unit digit of 634263 is the third digit in the cycle, which is 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.

Method 2: Using the properties of the unit digits

- The unit digit of 2 raised to any power follows a pattern: 2, 4, 8, 6, 2, 4, 8, 6, ...
- Therefore, the unit digit of 634262 is the same as the unit digit of 2 raised to the power of the unit digit of 634262.
- The unit digit of 634262 is 2, so we need to find the unit digit of 2² = 4.
- Similarly, the unit digit of 634263 is the same as the unit digit of 2 raised to the power of the unit digit of 634263.
- The unit digit of 634263 is 3, so we need to find the unit digit of 2³ = 8.
- Therefore, the unit digit of the product 634262 × 634263 is the product of the unit digits of 634262 and 634263, which is 4 × 8 = 32.
- The unit digit of 32 is 2.

Conclusion:

Using either method, we find that the unit digit of the product 634262 × 634263 is 2. Therefore, the correct answer is option 'A' (0).