To multiply \( \frac{4}{9} \) by \( -3 \), we can first rewrite \( -3 \) as a fraction:
\[ -3 = -\frac{3}{1} \]
Now we can multiply the fractions:
\[ \frac{4}{9} \times -\frac{3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]
Now we need to simplify \( \frac{-12}{9} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Now, to express \( \frac{-4}{3} \) as a mixed number, we can convert it:
\[ -4 \div 3 = -1 \quad \text{with a remainder of} \quad -1 \]
This means:
\[ -4 = -3 - 1 \]
Thus, we can express this as:
\[ -1\frac{1}{3} \]
So, the final answer as a mixed number in simplest form is:
\[ \boxed{-1 \frac{1}{3}} \]