To solve the inequality \(\frac{4}{5}d \leq 24\), we begin by isolating \(d\).
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Multiply both sides of the inequality by \(\frac{5}{4}\) to eliminate the fraction on the left side: \[ d \leq 24 \cdot \frac{5}{4} \]
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Calculate \(24 \cdot \frac{5}{4}\): \[ 24 \cdot \frac{5}{4} = 24 \cdot 1.25 = 30 \]
Thus, we have: \[ d \leq 30 \]
The solution to the inequality is \(d \leq 30\). Therefore, the answer is: \[ \boxed{30} \]