Multiply $15$ by $ \dfrac{a^2}{a^2+6a-16} $ to get $ \dfrac{ 15a^2 }{ a^2+6a-16 } $.

Step 1: Write $ 15 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 15 \cdot \frac{a^2}{a^2+6a-16} & \xlongequal{\text{Step 1}} \frac{15}{\color{red}{1}} \cdot \frac{a^2}{a^2+6a-16} \xlongequal{\text{Step 2}} \frac{ 15 \cdot a^2 }{ 1 \cdot \left( a^2+6a-16 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 15a^2 }{ a^2+6a-16 } \end{aligned} $$

Multiply $4$ by $ \dfrac{a}{3a} $ to get $ \dfrac{ 4a }{ 3a } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{15a^2}{a^2+6a-16} $ by $ 8 $ to get $ \dfrac{ 120a^2 }{ a^2+6a-16 } $.

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.

$$ \begin{aligned} \frac{15a^2}{a^2+6a-16} \cdot 8 & \xlongequal{\text{Step 1}} \frac{15a^2}{a^2+6a-16} \cdot \frac{8}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 15a^2 \cdot 8 }{ \left( a^2+6a-16 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 120a^2 }{ a^2+6a-16 } \end{aligned} $$

Multiply $4$ by $ \dfrac{a}{3a} $ to get $ \dfrac{ 4a }{ 3a } $.

Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{4a}{3a} $ from $ \dfrac{120a^2}{a^2+6a-16} $ to get $ \dfrac{ \color{purple}{ 356a^3-24a^2+64a } }{ 3a^3+18a^2-48a }$.

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}{ 3a }$ and the second by $\color{blue}{ a^2+6a-16 }$.

$$ \begin{aligned} \frac{120a^2}{a^2+6a-16} - \frac{4a}{3a} & = \frac{ 120a^2 \cdot \color{blue}{ 3a }}{ \left( a^2+6a-16 \right) \cdot \color{blue}{ 3a }} - \frac{ 4a \cdot \color{blue}{ \left( a^2+6a-16 \right) }}{ 3a \cdot \color{blue}{ \left( a^2+6a-16 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 360a^3 } }{ 3a^3+18a^2-48a } - \frac{ \color{purple}{ 4a^3+24a^2-64a } }{ 3a^3+18a^2-48a } = \\[1ex] &=\frac{ \color{purple}{ 360a^3 - \left( 4a^3+24a^2-64a \right) } }{ 3a^3+18a^2-48a }=\frac{ \color{purple}{ 356a^3-24a^2+64a } }{ 3a^3+18a^2-48a } \end{aligned} $$