Multiply $8$ by $ \dfrac{y}{12y+12} $ to get $ \dfrac{ 8y }{ 12y+12 } $.

Step 1: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 8 \cdot \frac{y}{12y+12} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} \cdot \frac{y}{12y+12} \xlongequal{\text{Step 2}} \frac{ 8 \cdot y }{ 1 \cdot \left( 12y+12 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 8y }{ 12y+12 } \end{aligned} $$

Multiply $10$ by $ \dfrac{y}{3y+3} $ to get $ \dfrac{ 10y }{ 3y+3 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{y}{3y+3} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{y}{3y+3} \xlongequal{\text{Step 2}} \frac{ 10 \cdot y }{ 1 \cdot \left( 3y+3 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10y }{ 3y+3 } \end{aligned} $$

Subtract $ \dfrac{10y}{3y+3} $ from $ \dfrac{8y}{12y+12} $ to get $ \dfrac{ \color{purple}{ -32y } }{ 12y+12 }$.

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

$$ \begin{aligned} \frac{8y}{12y+12} - \frac{10y}{3y+3} & = \frac{ 8y }{ 12y+12 } - \frac{ 10y \cdot \color{blue}{ 4 }}{ \left( 3y+3 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 8y } }{ 12y+12 } - \frac{ \color{purple}{ 40y } }{ 12y+12 }=\frac{ \color{purple}{ -32y } }{ 12y+12 } \end{aligned} $$