We are asked to find the mean of the given set of numbers. The mean is calculated by adding up all the numbers in the set and dividing the sum by the total number of values.
The given set of numbers is:
\[
4, 6, 8, 10, 12.
\]
1. Step 1: Calculate the Sum of the Numbers
Add all the numbers together:
\[
4 + 6 + 8 + 10 + 12 = 40.
\]
2. Step 2: Divide by the Number of Values
There are 5 numbers in the set, so divide the sum by 5:
\[
\text{Mean} = \frac{40}{5} = 8.
\]
Thus, the mean of the set of numbers is:
\[
\boxed{8}.
\]