Solution:

Given digits are 3, 5, 6, 7 and 8.

We need to find the number of integers greater than 6000 that can be formed using these digits without repetition.

Integers with thousands place as 6, 7 or 8:

We can select the thousands place in 3 ways (6, 7 or 8).

For the hundreds place, we can select any of the remaining 4 digits (3, 5, 7 or 8).

For the tens place, we can select any of the remaining 3 digits.

For the units place, we can select any of the remaining 2 digits.

Therefore, the number of integers with thousands place as 6, 7 or 8 = 3 × 4 × 3 × 2 = 72.

Integers with thousands place as 5:

We can select the thousands place as 5.

For the hundreds place, we can select any of the remaining 4 digits (3, 6, 7 or 8).

For the tens place, we can select any of the remaining 3 digits.

For the units place, we can select any of the remaining 2 digits.

Therefore, the number of integers with thousands place as 5 = 1 × 4 × 3 × 2 = 24.

Total number of integers:

Therefore, the total number of integers that can be formed = 72 + 24 = 96.

But we need to find the number of integers greater than 6000.

Out of the 96 integers, 24 integers have thousands place as 5 and the remaining 72 integers have thousands place as 6, 7 or 8.

So, we need to find the number of integers greater than 6000 that can be formed using the digits 3, 6, 7 and 8 without repetition.

Integers with thousands place as 6, 7 or 8:

For the hundreds place, we can select any of the remaining 3 digits (3, 7 or 8).

For the tens place, we can select any of the remaining 2 digits.

For the units place, we can select any of the remaining 1 digits.

Therefore, the number of integers with thousands place as 6, 7 or 8 = 3 × 3 × 2 × 1 = 18.

Integers with thousands place as 5:

For the hundreds place, we can select any of the remaining 3 digits (3, 7 or 8).

For the tens place, we can select any of the remaining 2 digits.

For the units place, we can select any of the remaining 1 digits.

Therefore, the number of integers with thousands place as 5 = 1 × 3 × 2 × 1 = 6.

Total number of integers greater than 6000:

Therefore, the total number of integers greater than 6000 that can be formed = 18 + 6 = 24.

Hence, the correct answer is 24.