Use the distributive property.

Add $ \dfrac{1}{3a-3} $ and $ \dfrac{a}{6} $ to get $ \dfrac{ \color{purple}{ 3a^2-3a+6 } }{ 18a-18 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 6 }$ and the second by $\color{blue}{ 3a-3 }$.

$$ \begin{aligned} \frac{1}{3a-3} + \frac{a}{6} & = \frac{ 1 \cdot \color{blue}{ 6 }}{ \left( 3a-3 \right) \cdot \color{blue}{ 6 }} + \frac{ a \cdot \color{blue}{ \left( 3a-3 \right) }}{ 6 \cdot \color{blue}{ \left( 3a-3 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 6 } }{ 18a-18 } + \frac{ \color{purple}{ 3a^2-3a } }{ 18a-18 }=\frac{ \color{purple}{ 3a^2-3a+6 } }{ 18a-18 } \end{aligned} $$

Multiply $ \dfrac{a^2-a+2}{6a-6} $ by $ 3 $ to get $ \dfrac{ 3a^2-3a+6 }{ 6a-6 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{a^2-a+2}{6a-6} \cdot 3 & \xlongequal{\text{Step 1}} \frac{a^2-a+2}{6a-6} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( a^2-a+2 \right) \cdot 3 }{ \left( 6a-6 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3a^2-3a+6 }{ 6a-6 } \end{aligned} $$