To calculate the variance of a set of numbers, follow these steps:

1. Find the mean (average) of the numbers.

2. Subtract the mean from each number and square the result.

3. Find the average of the squared differences.

Given the numbers: 2, 6, 8, 6, 2, and 6.

Step 1: Calculate the mean:

Mean = \(\frac{2 + 6 + 8 + 6 + 2 + 6}{6} = \frac{30}{6} = 5\).

Step 2: Subtract the mean, square the result:

(2 - 5)^2 = 9

(6 - 5)^2 = 1

(8 - 5)^2 = 9

(6 - 5)^2 = 1

(2 - 5)^2 = 9

(6 - 5)^2 = 1

Step 3: Find the average of the squared differences:

Average = \(\frac{9 + 1 + 9 + 1 + 9 + 1}{6} = \frac{30}{6} = 5\).

Therefore, the variance of the given numbers is 5.