1. **State the problem:** We have a point $P(-2, 3)$ that is translated to $P'(-6, -4)$. We need to find the translation rule. 2. **Recall the translation rule:** A translation moves a point $(x, y)$ to $(x + a, y + b)$ where $a$ and $b$ are the horizontal and vertical shifts respectively. 3. **Set up equations:** Given $P(x, y) = (-2, 3)$ and $P'(x', y') = (-6, -4)$, the translation rule is: $$x' = x + a$$ $$y' = y + b$$ 4. **Find $a$ and $b$:** $$-6 = -2 + a \implies a = -6 + 2 = -4$$ $$-4 = 3 + b \implies b = -4 - 3 = -7$$ 5. **Write the translation rule:** $$T(x, y) = (x - 4, y - 7)$$ 6. **Check the options:** The correct translation rule is $T(x - 4, y - 7)$.