Multiply $2$ by $ \dfrac{a}{4} $ to get $ \dfrac{ 2a }{ 4 } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{a}{4} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{a}{4} \xlongequal{\text{Step 2}} \frac{ 2 \cdot a }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 2a }{ 4 } \end{aligned} $$

Multiply $ \dfrac{2a}{4} $ by $ a $ to get $ \dfrac{ 2a^2 }{ 4 } $.

Step 1: Write $ a $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2a}{4} \cdot a & \xlongequal{\text{Step 1}} \frac{2a}{4} \cdot \frac{a}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 2a \cdot a }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2a^2 }{ 4 } \end{aligned} $$

Subtract $ \dfrac{3a-3}{a^2-a-6} $ from $ \dfrac{2a^2}{4} $ to get $ \dfrac{ \color{purple}{ 2a^4-2a^3-12a^2-12a+12 } }{ 4a^2-4a-24 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ a^2-a-6 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{2a^2}{4} - \frac{3a-3}{a^2-a-6} & = \frac{ 2a^2 \cdot \color{blue}{ \left( a^2-a-6 \right) }}{ 4 \cdot \color{blue}{ \left( a^2-a-6 \right) }} - \frac{ \left( 3a-3 \right) \cdot \color{blue}{ 4 }}{ \left( a^2-a-6 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 2a^4-2a^3-12a^2 } }{ 4a^2-4a-24 } - \frac{ \color{purple}{ 12a-12 } }{ 4a^2-4a-24 } = \\[1ex] &=\frac{ \color{purple}{ 2a^4-2a^3-12a^2 - \left( 12a-12 \right) } }{ 4a^2-4a-24 }=\frac{ \color{purple}{ 2a^4-2a^3-12a^2-12a+12 } }{ 4a^2-4a-24 } \end{aligned} $$