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