Multiply $ \dfrac{1}{n+6} $ by $ \dfrac{n^2-4n-60}{2} $ to get $ \dfrac{ n-10 }{ 2 } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{n+6} \cdot \frac{n^2-4n-60}{2} & \xlongequal{\text{Step 1}} \frac{ 1 }{ 1 \cdot \color{red}{ \left( n+6 \right) } } \cdot \frac{ \left( n-10 \right) \cdot \color{red}{ \left( n+6 \right) } }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 }{ 1 } \cdot \frac{ n-10 }{ 2 } \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( n-10 \right) }{ 1 \cdot 2 } \xlongequal{\text{Step 4}} \frac{ n-10 }{ 2 } \end{aligned} $$