We are asked to factor the expression $\sin^2 \theta - \sin \theta - 12$.

1. Problem Description

We are asked to factor the expression $\sin^2 \theta - \sin \theta - 12$.

2. Solution Steps

Let $x = \sin \theta$. Then the expression becomes $x^2 - x - 12$.

We need to find two numbers that multiply to $-12$ and add to $-1$. These numbers are $-4$ and $3$.

So we can factor the expression as $(x - 4)(x + 3)$.

Substituting $x = \sin \theta$ back into the expression, we get $(\sin \theta - 4)(\sin \theta + 3)$.

3. Final Answer

The factored expression is $(\sin \theta - 4)(\sin \theta + 3)$.

So the correct answer is $(\sin \theta + 3)(\sin \theta - 4)$.