Add $x$ and $ \dfrac{7}{12} $ to get $ \dfrac{ \color{purple}{ 12x+7 } }{ 12 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 12 }$.

$$ \begin{aligned} x+ \frac{7}{12} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} + \frac{7}{12} = \frac{ x \cdot \color{blue}{ 12 }}{ 1 \cdot \color{blue}{ 12 }} + \frac{ 7 }{ 12 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 12x } }{ 12 } + \frac{ \color{purple}{ 7 } }{ 12 }=\frac{ \color{purple}{ 12x+7 } }{ 12 } \end{aligned} $$

Multiply $56$ by $ \dfrac{12x+7}{12} $ to get $ \dfrac{ 672x+392 }{ 12 } $.

Step 1: Write $ 56 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 56 \cdot \frac{12x+7}{12} & \xlongequal{\text{Step 1}} \frac{56}{\color{red}{1}} \cdot \frac{12x+7}{12} \xlongequal{\text{Step 2}} \frac{ 56 \cdot \left( 12x+7 \right) }{ 1 \cdot 12 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 672x+392 }{ 12 } \end{aligned} $$