To multiply \( \frac{4}{9} \) by \( -3 \), we can rewrite \( -3 \) as a fraction, which is \( -\frac{3}{1} \).
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 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, we need to convert \( -\frac{4}{3} \) into a mixed number.
Since \( -\frac{4}{3} \) can be expressed as \( -1 \frac{1}{3} \) (because 4 divided by 3 is 1 with a remainder of 1), we can write:
\[ -\frac{4}{3} = -1 \frac{1}{3} \]
Thus, the answer in mixed number form is
\[ \boxed{-1 \frac{1}{3}} \]