Since $f$ is a linear function, the difference between any two function values is proportional to the difference in the input values.
In other words, $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ is constant for any two input values $x_1$ and $x_2$.
Therefore, we have $\frac{f(6) - f(2)}{6 - 2} = \frac{12}{4} = 3$.
Now, we can use this proportion to find $f(12) - f(2)$.
We have $\frac{f(12) - f(2)}{12 - 2} = \frac{f(6) - f(2)}{6 - 2} = 3$.
Simplifying, we get $f(12) - f(2) = 3 \cdot 10 = \boxed{30}$.
The answer is: 30
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $f$ is a linear function and $f(6) - f(2) = 12$, what is the value of $f(12) - f(2)$?

### Answer:
