Multiply $6$ by $ \dfrac{a}{a+4} $ to get $ \dfrac{ 6a }{ a+4 } $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $11$ by $ \dfrac{a}{a-1} $ to get $ \dfrac{ 11a }{ a-1 } $.

Step 1: Write $ 11 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 11 \cdot \frac{a}{a-1} & \xlongequal{\text{Step 1}} \frac{11}{\color{red}{1}} \cdot \frac{a}{a-1} \xlongequal{\text{Step 2}} \frac{ 11 \cdot a }{ 1 \cdot \left( a-1 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 11a }{ a-1 } \end{aligned} $$

Subtract $ \dfrac{11a}{a-1} $ from $ \dfrac{6a}{a+4} $ to get $ \dfrac{ \color{purple}{ -5a^2-50a } }{ a^2+3a-4 }$.

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}{ a-1 }$ and the second by $\color{blue}{ a+4 }$.

$$ \begin{aligned} \frac{6a}{a+4} - \frac{11a}{a-1} & = \frac{ 6a \cdot \color{blue}{ \left( a-1 \right) }}{ \left( a+4 \right) \cdot \color{blue}{ \left( a-1 \right) }} - \frac{ 11a \cdot \color{blue}{ \left( a+4 \right) }}{ \left( a-1 \right) \cdot \color{blue}{ \left( a+4 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 6a^2-6a } }{ a^2-a+4a-4 } - \frac{ \color{purple}{ 11a^2+44a } }{ a^2-a+4a-4 } = \\[1ex] &=\frac{ \color{purple}{ 6a^2-6a - \left( 11a^2+44a \right) } }{ a^2+3a-4 }=\frac{ \color{purple}{ -5a^2-50a } }{ a^2+3a-4 } \end{aligned} $$