Multiply $ \dfrac{9}{16} $ by $ x $ to get $ \dfrac{ 9x }{ 16 } $.

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.

$$ \begin{aligned} \frac{9}{16} \cdot x & \xlongequal{\text{Step 1}} \frac{9}{16} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x }{ 16 } \end{aligned} $$

Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $.

Multiply $ \dfrac{9}{16} $ by $ x $ to get $ \dfrac{ 9x }{ 16 } $.

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.

$$ \begin{aligned} \frac{9}{16} \cdot x & \xlongequal{\text{Step 1}} \frac{9}{16} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 16 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x }{ 16 } \end{aligned} $$

Subtract $ \dfrac{1}{3} $ from $ \dfrac{9x}{16} $ to get $ \dfrac{ \color{purple}{ 27x-16 } }{ 48 }$.

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}{ 3 }$ and the second by $\color{blue}{ 16 }$.

$$ \begin{aligned} \frac{9x}{16} - \frac{1}{3} & = \frac{ 9x \cdot \color{blue}{ 3 }}{ 16 \cdot \color{blue}{ 3 }} - \frac{ 1 \cdot \color{blue}{ 16 }}{ 3 \cdot \color{blue}{ 16 }} = \\[1ex] &=\frac{ \color{purple}{ 27x } }{ 48 } - \frac{ \color{purple}{ 16 } }{ 48 }=\frac{ \color{purple}{ 27x-16 } }{ 48 } \end{aligned} $$