$$ 6-\frac{-4}{12} = 6 \cdot \color{blue}{\frac{ 12 }{ 12}} - \frac{-4}{12} \cdot \color{blue}{\frac{ 1 }{ 1}} = \frac{72+4}{12} $$

Simplify numerator

$$ \color{blue}{72} + \color{blue}{4} = \color{blue}{76} $$

Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $.

Subtract $-8$ from $ \dfrac{19}{3} $ to get $ \dfrac{ \color{purple}{ 43 } }{ 3 }$.

Step 1: Write $ -8 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{3}$.

$$ \begin{aligned} \frac{19}{3} --8 & \xlongequal{\text{Step 1}} \frac{19}{3} - \frac{-8}{\color{red}{1}} = \frac{ 19 }{ 3 } - \frac{ \left( -8 \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 19 } }{ 3 } - \frac{ \color{purple}{ -24 } }{ 3 }=\frac{ \color{purple}{ 43 } }{ 3 } \end{aligned} $$