Multiply $3$ by $ \dfrac{y}{6y+1} $ to get $ \dfrac{ 3y }{ 6y+1 } $.

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.

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

Subtract $9y+2$ from $ \dfrac{3y}{6y+1} $ to get $ \dfrac{ \color{purple}{ -54y^2-18y-2 } }{ 6y+1 }$.

Step 1: Write $ 9y+2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{6y+1}$.

$$ \begin{aligned} \frac{3y}{6y+1} -9y+2 & \xlongequal{\text{Step 1}} \frac{3y}{6y+1} - \frac{9y+2}{\color{red}{1}} = \frac{ 3y }{ 6y+1 } - \frac{ \left( 9y+2 \right) \cdot \color{blue}{ \left( 6y+1 \right) }}{ 1 \cdot \color{blue}{ \left( 6y+1 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3y } }{ 6y+1 } - \frac{ \color{purple}{ 54y^2+9y+12y+2 } }{ 6y+1 }=\frac{ \color{purple}{ 3y - \left( 54y^2+9y+12y+2 \right) } }{ 6y+1 } = \\[1ex] &=\frac{ \color{purple}{ -54y^2-18y-2 } }{ 6y+1 } \end{aligned} $$