jmc

Since $f$ is a linear function, its slope is constant. Therefore

$$\frac{f(6)-f(2)}{6-2}=\frac{f(12)-f(2)}{12-2},$$so $$\frac{12}{4}=\frac{f(12)-f(2)}{10},$$and $f(12)-f(2)=\boxed{30}$.