To multiply \(\frac{4}{9}\) by \(-3\), we start by writing \(-3\) 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 \(\frac{-12}{9}\). We can divide both the numerator and the denominator 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 divide \(4\) by \(3\):
- \(4\) divided by \(3\) gives \(1\) with a remainder of \(1\).
So, we can write this as:
\[ -1 \frac{1}{3} \]
Therefore, the final answer is:
\[ \boxed{-1 \frac{1}{3}} \]