Choice C is correct. It's given that the cherry pitting machine pits $12$ pounds of cherries in $3$ minutes. This rate can be written as $StartFraction 12 pounds of cherries Over 3 minutes EndFraction$ . 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 $\frac{12 pounds of cherries}{3 minutes} = \frac{96 pounds of cherries}{x minutes}$ , which can be rewritten as $\frac{12}{3} = \frac{96}{x}$ , or $4 = \frac{96}{x}$ . Multiplying each side of this equation by $x$ yields $4 x equals 96$ . Dividing each side of this equation by $4$ yields $x equals 24$ . 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.