What digit can be written in place of x so that 4508𝑥 number divisible by 12?

Solution:
1. A number is divisible by 12 if and only if it is divisible by both 3 and 4.
2. Check divisibility by 4:
- The last two digits of the number 4508x must be divisible by 4.
- Possible last two digits can be 80, 81, 82, 83, 84, 85, 86, 87, 88, \text{or} 89.
- From these, 80, 84, \text{and} 88 are divisible by 4.

3. Check divisibility by 3:
- The sum of the digits of the number 4508x must be divisible by 3.
- The sum of the digits 4 + 5 + 0 + 8 = 17.
- We seek x such that 17 + x is divisible by 3.

4. Check which x among 0, 4, 8 makes 17 + x divisible by 3:
- If x = 0, then 17 + 0 = 17 (not divisible by 3)
- If x = 4, then 17 + 4 = 21 (divisible by 3)
- If x = 8, then 17 + 8 = 25 (not divisible by 3)

5. The digit x that makes 4508x divisible by 12 is 4.