To multiply the fraction \( \frac{4}{9} \) by \( -3 \), you can convert \( -3 \) into a fraction:
\[ -3 = \frac{-3}{1} \]
Now, multiply the fractions:
\[ \frac{4}{9} \times \frac{-3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]
Next, simplify \( \frac{-12}{9} \). Both the numerator and the denominator can be divided by 3:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Now, convert \( \frac{-4}{3} \) into a mixed number. Since \(-4\) is less than \(-3\), we can express it as:
\[ -4 = -1 \cdot 3 + -1 \]
So as a mixed number, this is:
\[ -1 \frac{1}{3} \]
Therefore, the answer is:
\[ -\frac{4}{3} \text{ or } -1 \frac{1}{3} \]
in simplest form.