Solution:

We have to form the integers greater than 6,000 using the digits 3, 5, 6, 7 and 8 without repetition.

To form an integer greater than 6,000, the first digit cannot be 3 or 5. Therefore, we have three cases:

Case 1: First digit is 6
In this case, we have four choices for the second digit, three choices for the third digit, two choices for the fourth digit, and one choice for the fifth digit.
Total number of integers = 4 x 3 x 2 x 1 = 24

Case 2: First digit is 7
In this case, we have three choices for the second digit (as we cannot repeat 6), three choices for the third digit, two choices for the fourth digit, and one choice for the fifth digit.
Total number of integers = 3 x 3 x 2 x 1 = 18

Case 3: First digit is 8
In this case, we have three choices for the second digit (as we cannot repeat 6 or 7), two choices for the third digit, one choice for the fourth digit, and one choice for the fifth digit.
Total number of integers = 3 x 2 x 1 x 1 = 6

Therefore, the total number of integers greater than 6,000 that can be formed without repetition is:
24 + 18 + 6 = 48 + 18 = 66

However, we have counted the integer 6,789 twice (in Case 1 and Case 2). Therefore, we need to subtract 1 from the total number of integers.

Total number of integers = 66 - 1 = 65

Since we need to count only the integers greater than 6,000, we need to subtract the integers that start with 6 from the total.

Number of integers that start with 6 = 4 x 3 x 2 x 1 = 24

Therefore, the final answer is 65 - 24 = 41.

Hence, the correct option is (B) 192.