Recall the formula for the area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees): it involves the fraction $\theta/360$ multiplied by the area of the full circle $\pi r^2$.

Substitute $r = 12$ and $\theta = 150$ into the sector area formula. Simplify $12^2$ and reduce the fraction $150/360$ before multiplying to keep the arithmetic easy.

In Desmos, type the expression (150/360)*pi*12^2 and press Enter. Compare the simplified symbolic result shown by Desmos to the answer choices; the matching expression is the correct choice.

For a circle with radius $r$ and a sector with central angle $\theta$ degrees, the area $A$ of the sector is

This formula says: take the fraction of the full circle ($\theta/360$) and multiply by the area of the whole circle ($\pi r^2$).

Here, the radius is $r=12$ centimeters and the central angle is $\theta = 150^\circ$.

Substitute these into the formula:

Calculate $12^2$:

So the expression becomes

First reduce the fraction $\frac{150}{360}$:

Now multiply this by $144\pi$:

Compute $\frac{144}{12} = 12$, so

So the area of the sector is $60\pi$ square centimeters, which corresponds to choice C.