We start by writing the problem in vertical form: $$\begin{array}{r} 12{\textstyle{2 \over 9}}\\ \underline { - 8{\textstyle{4 \over 9}}} \end{array}$$ Notice that the top fraction is smaller than the bottom fraction. This means that we will need to borrow $1$ from the top whole number, $12\text{,}$ and add it to the top fraction, making it an improper fraction. Then, we subtract the bottom fraction from the new top fraction, as well subtract the whole numbers, as shown below: $$\underline{ \begin{array}{r} 11 + 1 + {\textstyle{2 \over 9}}\\ - 8{\textstyle{4 \over 9}} \end{array} }$$ Now we have, $$\underline{ \begin{array}{r} 11 + {\textstyle{9 \over 9}} + {\textstyle{2 \over 9}}\\ - 8{\textstyle{4 \over 9}} \end{array} }$$ Finally, we can subtract, $$\begin{array}{r} 11{\textstyle{11 \over 9}}\\ \underline { - 8{\textstyle{4 \over 9}}} \\ 3{\textstyle{7 \over 9}} \end{array}$$ Since the fraction is already reduced, we are finished. Therefore, $12\,\frac{2}{9}-8\,\frac{4}{9}=3\,\frac{7}{9}\text{.}$