Find the total area of the shaded region bounded by the following curves. \[ \begin{array}{l} x=36 y^{2}-12 y^{3} \\ x=6 y^{2}-18 y \end{array} \]

Step 1 ：We are given two curves, \(x=36 y^{2}-12 y^{3}\) and \(x=6 y^{2}-18 y\).

Step 2 ：The area between two curves is given by the integral of the absolute difference between the two functions.

Step 3 ：We first need to find the points of intersection of the two curves to determine the limits of integration.

Step 4 ：The points of intersection are \(-\frac{1}{2}\), 0, and 3.

Step 5 ：By integrating the absolute difference between the two functions over these limits, we find that the total area of the shaded region is \(\frac{13}{16}\).

Step 6 ：Final Answer: The total area of the shaded region bounded by the curves \(x=36 y^{2}-12 y^{3}\) and \(x=6 y^{2}-18 y\) is \(\boxed{\frac{13}{16}}\).