Vimala was asked to simplify the expression \(3d(6d^{3} - 5d + 9)\).
She wrote the result as \(18d^{3} - 15d + 27d\)
However, her teacher marked her answer incorrect.
Based on the situation, answer the following questions.
1. What should be the correct expansion of \(3d(6d^{3} - 5d + 9)\)?
2. What error did Nilan make while multiplying the expressions?
3. Which rule should he use to rectify his mistake?
4. What is the highest degree of \(d\) in the correct expansion?