To solve for \( u \) in the equation
\[
- \frac{4}{9}u = 24, \]
first, isolate \( u \) by multiplying both sides of the equation by the reciprocal of \( -\frac{4}{9} \). The reciprocal of \( -\frac{4}{9} \) is \( -\frac{9}{4} \).
Multiply both sides by \( -\frac{9}{4} \):
\[ u = 24 \times -\frac{9}{4}. \]
Now calculate the right-hand side:
\[ u = -\frac{9 \times 24}{4}. \]
Simplifying \( \frac{24}{4} \) gives \( 6 \):
\[ u = -9 \times 6. \]
Now multiply:
\[ u = -54. \]
Thus, the solution is
\[ \boxed{-54}. \]
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