To multiply \( \frac{4}{9} \) by \(-3\), we can write \(-3\) as a fraction: \(-3\) can be expressed as \(-\frac{3}{1}\). Now we can multiply the fractions:
\[ \frac{4}{9} \times -\frac{3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]
Next, we can simplify \(\frac{-12}{9}\). To do this, we find the greatest common divisor (GCD) of 12 and 9, which is 3. Then we divide both the numerator and the denominator by their GCD:
\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]
Now, to express \(\frac{-4}{3}\) as a mixed number, we note that \(-4\) divided by \(3\) gives us \(-1\) with a remainder of \(-1\):
\[ -4 \div 3 = -1\quad \text{(remainder 1)} \]
Thus, we can express \(-\frac{4}{3}\) as:
\[ -1 \frac{1}{3} \]
Therefore, the answer is:
\[ \boxed{-1 \frac{1}{3}} \]