Simple - 3,6,8,0 without repetition is 8630
With repetition= 8860
Without repetition= 8630

The greatest four-digit number using digits 3, 6, 8, and 0 without repetition is 8630.

Explanation:

Step 1: Understanding the question
To find the greatest four-digit number using the given digits (3, 6, 8, and 0) without repetition, we need to arrange these digits in a way that produces the largest possible number.

Step 2: Analyzing the options
Let's analyze each option to see which one gives us the greatest four-digit number:

a) 0368: This number starts with 0, which is not ideal since the greatest four-digit number cannot start with 0.

b) 3068: This number also starts with 0, which is not ideal.

c) 8630: This number does not start with 0 and contains the digits 3, 6, 8, and 0 without repetition. It seems like a potential candidate for the greatest four-digit number.

d) 6830: This number also does not start with 0 and contains the digits 3, 6, 8, and 0 without repetition. However, it is smaller than option c (8630).

Step 3: Comparing the options
Comparing options c (8630) and d (6830), we can see that the digit 8 is in the thousands place in option c, while it is in the hundreds place in option d. Since the thousands place has a higher place value, putting the largest digit (8) in that position will result in a greater number.

Step 4: Conclusion
Therefore, the option c (8630) is the correct answer as it gives us the greatest four-digit number using the digits 3, 6, 8, and 0 without repetition.