Choice C is correct. It’s given that the cherry pitting machine pounds $12$ pounds of cherries in $3$ minutes. This rate can be written as $\dfrac{12 pounds of cherries}{3 minutes}$ .If the number of minutes it takes the machine to pit $96$ pounds of cherries is represented by $x$, the value of $x$ can be calculated by solving the equation $\dfrac{12 pounds of cherries}{3 minutes} = \dfrac{96 pounds of cherries}{x minutes}$, which can be rewritten as $\dfrac{12}{3} = \dfrac{96}{z}$, or $4 = \dfrac{96}{z}$. Multiplying each side of this equation by $x$ yields $4x$ = $96$. Dividing each side of this equation by $4$ yields $x = 24$. Therefore, it takes the machine $24$ minutes to pit $96$ pounds of cherries.

Choice A is incorrect. This is the number of minutes it takes the machine to pit $32$ , not $96$, pounds of cherries.

Choice B is incorrect. This is the number of minutes it takes the machine to pit $60$ , not $96$, pounds of cherries.

Choice D is incorrect. This is the number of minutes it takes the machine to pit $144$ , not $96$, pounds of cherries.