Find the area of the region enclosed by the curves $y=x^{2}-3$ and $y=6$.

Step 1 ：First, we need to find the intersection points of the two curves. We can do this by setting \(x^{2}-3 = 6\) and solving for \(x\).

Step 2 ：By solving the equation, we find that the intersection points are \(x = -3\) and \(x = 3\).

Step 3 ：Next, we calculate the area between the two curves. The area between two curves is given by the integral of the absolute difference between the two functions, evaluated from the leftmost to the rightmost intersection points of the two curves.

Step 4 ：In this case, we integrate the absolute difference between the two functions from \(x = -3\) to \(x = 3\).

Step 5 ：By performing the integration, we find that the area between the two curves is 36 square units.

Step 6 ：Final Answer: The area of the region enclosed by the curves \(y=x^{2}-3\) and \(y=6\) is \(\boxed{36}\) square units.