Find the total area of the shaded region bounded by the following curves. \[ \begin{array}{l} x=8 y^{2}-8 y^{3} \\ x=6 y^{2}-6 y \end{array} \] Set up the integral that gives the area of the shaded region.

Step 1 ：First, we need to find the intersection points of the two curves. We set \(8y^2 - 8y^3 = 6y^2 - 6y\).

Step 2 ：Solving the equation, we get \(2y^2 - 2y^3 = 0\). Factoring out \(2y^2\), we get \(2y^2(1 - y) = 0\).

Step 3 ：Setting each factor equal to zero gives us \(y = 0\) and \(y = 1\).

Step 4 ：The area of the shaded region is given by the integral of the absolute difference of the two functions from \(y = 0\) to \(y = 1\).

Step 5 ：So, the integral is \(\int_{0}^{1} |8y^2 - 8y^3 - (6y^2 - 6y)| dy\).

Step 6 ：Simplifying the integrand, we get \(\int_{0}^{1} |2y^2 - 2y^3 + 6y| dy\).

Step 7 ：We can split the integral into two parts: \(\int_{0}^{1} 2y^2 dy + \int_{0}^{1} -2y^3 dy + \int_{0}^{1} 6y dy\).

Step 8 ：Evaluating the integrals, we get \(\frac{2}{3} - \frac{1}{2} + 3 = \frac{7}{6}\).

Step 9 ：So, the total area of the shaded region is \(\boxed{\frac{7}{6}}\).