jmc

Let's write down all the possibilities, simplify the resulting fractions, and count the number of values we can achieve. $$\frac{4}{4}=1\frac{4}{8}=\frac{1}{2}\frac{4}{12}=\frac{1}{3}$$$$\frac{8}{4}=2\frac{8}{8}=1\frac{8}{12}=\frac{2}{3}$$$$\frac{12}{4}=3\frac{12}{8}=\frac{3}{2}\frac{12}{12}=1.$$We can get 1, 2, 3, 1/2, 3/2, 1/3 and 2/3, for a total of $\boxed{7}$ different values.