Find the smallest 4-digit number divisible by 8, formed using the digits 0, 2, 3, 4, 6, 8 without any repetition.

We need to find the smallest 4-digit number using the digits $\{0,2,3,4,6,8\}$ without repetition, which is divisible by 8.The divisibility rule for 8 states that the number formed by the last three digits must be divisible by 8.Let's inspect the given options from smallest to largest to easily find the smallest valid number:2034: 4-digit number, but the last digit is 4, which is even. Let's check the last 3 digits: 034. 34 is not divisible by 8. Thus, 2034 is not divisible by 8.2048: Let's check if it uses the given digits: 2, 0, 4, 8 are all in the set, and there is no repetition.Check divisibility by 8: $\frac{2048}{8}=256$, which is perfectly divisible.Since 2048 is the smallest numerical value among the options containing valid digits starting with the smallest possible non-zero digit (2), it is the correct answer.