jmc

Let $x=.\overline{6}$. Multiplying both sides by 10, we get $10x=6.\overline{6}$. Subtracting these equations yields $9x=6$, so $x=\frac{6}{9}=\frac{2}{3}$. Substituting this into our original expression, we get $$(.\overline{6})(3)=\left(\frac{2}{3}\right)(3)=\left(\frac{2}{\cancel{3}}\right)(\cancel{3})=\boxed{2}.$$