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 $ \dfrac{15a^2}{a^2+6a-16} $ by $ \dfrac{8-4a}{3a} $ to get $ \dfrac{ -60a^2 }{ 3a^2+24a } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{15a^2}{a^2+6a-16} \cdot \frac{8-4a}{3a} & \xlongequal{\text{Step 1}} \frac{ 15a^2 }{ \left( a+8 \right) \cdot \color{red}{ \left( a-2 \right) } } \cdot \frac{ \left( -4 \right) \cdot \color{red}{ \left( a-2 \right) } }{ 3a } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 15a^2 }{ a+8 } \cdot \frac{ -4 }{ 3a } \xlongequal{\text{Step 3}} \frac{ 15a^2 \cdot \left( -4 \right) }{ \left( a+8 \right) \cdot 3a } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ -60a^2 }{ 3a^2+24a } \end{aligned} $$