1. **State the problem:** We need to find the right-hand limit of the function $f(x)$ as $x$ approaches $-4$ from the right, denoted as $\lim_{x \to -4^+} f(x)$. 2. **Understand the function behavior:** The function is piecewise. For $x > -4$, $f(x)$ is a downward-opening parabola passing through $(-3,0)$ and has an open circle at $(-4,-6)$. For $x \leq -4$, it is a line with a downward slope intersecting at $(-4,-6)$. 3. **Right-hand limit definition:** The right-hand limit $\lim_{x \to -4^+} f(x)$ considers values of $x$ slightly greater than $-4$. So we focus on the parabola part of the function. 4. **Evaluate the limit:** Since the parabola has an open circle at $(-4,-6)$, the function does not take the value $-6$ at $x=-4$ from the right side. Instead, the limit is the $y$-value the parabola approaches as $x$ approaches $-4$ from the right. 5. **Using the point $(-3,0)$ and the shape:** The parabola passes through $(-3,0)$ and approaches $(-4,-6)$ but does not include it. The limit from the right is the $y$-value the parabola approaches at $x=-4$, which is $-6$. 6. **Conclusion:** Therefore, $$\lim_{x \to -4^+} f(x) = -6.$$