To multiply the fraction \( \frac{4}{9} \) 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 \( \frac{-12}{9} \). The greatest common divisor (GCD) of 12 and 9 is 3.
Now, dividing the numerator and the denominator by their GCD:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Since \( -4 \) is greater than \( -3 \), we can convert \( \frac{-4}{3} \) into a mixed number.
To do this, we divide -4 by 3:
\[ -4 \div 3 = -1 \quad \text{(whole number)} \] with a remainder:
\[ -4 - (-1 \times 3) = -4 + 3 = -1 \]
So, we have:
\[ -4 = -1 \frac{1}{3} \]
Thus, the final answer is:
\[ -1 \frac{1}{3} \]
So, the answer is:
\(\boxed{-1 \frac{1}{3}}\)