Use the distributive property.

Combine like terms

Multiply $ \dfrac{14}{9} $ by $ x $ to get $ \dfrac{ 14x }{ 9 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{14}{9} \cdot x & \xlongequal{\text{Step 1}} \frac{14}{9} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 14 \cdot x }{ 9 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14x }{ 9 } \end{aligned} $$

Subtract $63$ from $ \dfrac{14x}{9} $ to get $ \dfrac{ \color{purple}{ 14x-567 } }{ 9 }$.

Step 1: Write $ 63 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{9}$.

$$ \begin{aligned} \frac{14x}{9} -63 & \xlongequal{\text{Step 1}} \frac{14x}{9} - \frac{63}{\color{red}{1}} = \frac{ 14x }{ 9 } - \frac{ 63 \cdot \color{blue}{ 9 }}{ 1 \cdot \color{blue}{ 9 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 14x } }{ 9 } - \frac{ \color{purple}{ 567 } }{ 9 }=\frac{ \color{purple}{ 14x-567 } }{ 9 } \end{aligned} $$