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The correct answer is $24$. The equation $\frac{24x}{ny}=4$ can be rewritten as $\left(\frac{24}{n}\right)\left(\frac{x}{y}\right)=4$. It's given that $\frac{x}{y}=4$. Substituting $4$ for $\frac{x}{y}$ in the equation $\left(\frac{24}{n}\right)\left(\frac{x}{y}\right)=4$ yields $\left(\frac{24}{n}\right)\left(4\right)=4$. Multiplying both sides of this equation by $n$ yields $\left(24\right)\left(4\right)=4n$. Dividing both sides of this equation by $4$ yields $24=n$. Therefore, the value of $n$ is $24$.