Multiply $3x$ by $ \dfrac{y}{6y^4} $ to get $ \dfrac{ 3xy }{ 6y^4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3x \cdot \frac{y}{6y^4} & \xlongequal{\text{Step 1}} \frac{3x}{\color{red}{1}} \cdot \frac{y}{6y^4} \xlongequal{\text{Step 2}} \frac{ 3x \cdot y }{ 1 \cdot 6y^4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3xy }{ 6y^4 } \end{aligned} $$

Add $ \dfrac{10x^3y^4}{15x} $ and $ \dfrac{3xy}{6y^4} $ to get $ \dfrac{ \color{purple}{ 60x^3y^8+45x^2y } }{ 90xy^4 }$.

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}{ 6y^4 }$ and the second by $\color{blue}{ 15x }$.

$$ \begin{aligned} \frac{10x^3y^4}{15x} + \frac{3xy}{6y^4} & = \frac{ 10x^3y^4 \cdot \color{blue}{ 6y^4 }}{ 15x \cdot \color{blue}{ 6y^4 }} + \frac{ 3xy \cdot \color{blue}{ 15x }}{ 6y^4 \cdot \color{blue}{ 15x }} = \\[1ex] &=\frac{ \color{purple}{ 60x^3y^8 } }{ 90xy^4 } + \frac{ \color{purple}{ 45x^2y } }{ 90xy^4 }=\frac{ \color{purple}{ 60x^3y^8+45x^2y } }{ 90xy^4 } \end{aligned} $$