Answer
Amelia was wrong because she did not write the equation in the form $x^2+bx+c=0$ .
The solution set is $\left\{0, \frac{3}{2}\right\}$.
Work Step by Step
Amelia was wrong because she did not write the equation in the form $x^2+bx+c=0$ before factoring. The Zero-Product Property can only be used for equations in the form $ab=0$.
The correct work is the one below:
\begin{align*}
4x^2-6x&=0\\
2x(2x-3)&=0\\
2x&=0 &\text{or}& &2x-3=0\\
x&=0 &\text{or}& &x=\frac{3}{2}\end{align*}