Here is the sketch of the region enclosed by the curves $y = |6x|$ (blue line) and $y = x^2 - 7$ (red curve). The shaded purple area represents the enclosed region between the two curves.

Would you like further details on the calculations or any additional questions?

Here are five related questions you might find interesting:

1. How do you calculate the area of the enclosed region using integration?
2. What happens to the enclosed region if the parabola is shifted further downwards?
3. How would the graph change if the absolute value function was modified to $y = |3x|$?
4. Can you find the points of intersection graphically without solving algebraically?
5. How does the symmetry of these curves affect the enclosed region?

Tip: When sketching curves, always start by identifying key features like intersections, vertices, and axes intercepts.