Here is the graph of the system of equations:

• The quadratic equation $y = (x - 4)^2 - 8$ is represented by the upward-opening parabola.
• The linear equation $y = -x - 6$ is shown as a straight line.

By observing the graph, you can see that the line intersects the parabola at two points. This indicates that the system of equations has two solutions.

Would you like to go over how to solve this algebraically, or do you have any other questions related to this? Here's some additional info you might find helpful:

Related Questions:

1. How do we solve a system of quadratic and linear equations algebraically?
2. What are the properties of a quadratic function that influence how it intersects with a linear equation?
3. How can we find the exact intersection points of these equations algebraically?
4. What would happen if the line was parallel to the parabola instead of intersecting it?
5. How do you interpret the number of solutions in a real-world context?

Tip: Always start by plotting the vertex of the parabola when graphing a quadratic equation in vertex form. It helps to visualize the curve and locate the direction it opens in!