8. The curve \(C\) has equation
$$y = ( x - 2 ) ( x - 4 ) ^ { 2 }$$
- Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - 20 x + 32$$
The line \(l _ { 1 }\) is the tangent to \(C\) at the point where \(x = 6\)
- Find the equation of \(l _ { 1 }\), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.
The line \(l _ { 2 }\) is the tangent to \(C\) at the point where \(x = \alpha\)
Given that \(l _ { 1 }\) and \(l _ { 2 }\) are parallel and distinct, - find the value of \(\alpha\)