To solve this problem, we need to calculate the probability that the sum of the numbers on four dice is equal to 6.

Each die has 6 faces, numbered from 1 to 6. When four dice are rolled, there are a total of \(6^4\) possible outcomes. This is because each die operates independently and can land on any of one six faces.

Therefore, the total number of outcomes from rolling four dice is:

\(6^4 = 1296\)

Next, we determine the number of favorable outcomes, i.e., the combinations where the sum equals 6.

The possible ways to get the sum of 6 when four numbers (from 1 to 6) are added is important because each die can contribute to the total in various ways, but we need to ensure that their total is exactly 6. The outcomes can be visualized as:

• (1, 1, 1, 3)
• (1, 1, 2, 2)
• (1, 2, 1, 2)
• (1, 2, 2, 1)
• (2, 1, 1, 2)
• (2, 1, 2, 1)
• (2, 2, 1, 1)
• (3, 1, 1, 1)

Notice that these combinations need to include permutations. Let's calculate the number of permutations for each favorable outcome:

• (1, 1, 1, 3) - 4 permutations
• (1, 1, 2, 2) - 6 permutations
• (1, 2, 1, 2) - 6 permutations (similar to (1, 1, 2, 2))
• (2, 2, 1, 1) - 6 permutations (similar to (1, 1, 2, 2))
• (3, 1, 1, 1) - 4 permutations

Therefore, the total number of favorable permutations equals:

\(4 + 6 + 6 + 6 + 4 = 26\)

Thus, the probability of getting a total of 6 is:

\(\frac{26}{1296} = \frac{2}{648} = \frac{5}{648}\)

This matches the correct answer, which is \(\frac{5}{648}\).