In a sequence of consecutive integers, the sum of the first four integers and the sum of the last four integers will have the same difference because they have an equal number of terms, and each term in the sum of the last four integers is greater by a fixed value compared to the corresponding term in the sum of the first four integers.

For example, consider the sequence of consecutive integers: 1, 2, 3, 4, 5, 6, 7, 8. The sum of the first four integers (1 + 2 + 3 + 4) is 10, and the sum of the last four integers (5 + 6 + 7 + 8) is 26. The difference between these two sums is 26 - 10 = 16.

So, the sum of the last four integers is 16 greater than the sum of the first four integers. Therefore, the answer is indeed 16.