Add $6$ and $ \dfrac{1}{2x^2} $ to get $ \dfrac{ \color{purple}{ 12x^2+1 } }{ 2x^2 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{ 2x^2 }$.

$$ \begin{aligned} 6+ \frac{1}{2x^2} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} + \frac{1}{2x^2} = \frac{ 6 \cdot \color{blue}{ 2x^2 }}{ 1 \cdot \color{blue}{ 2x^2 }} + \frac{ 1 }{ 2x^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 12x^2 } }{ 2x^2 } + \frac{ \color{purple}{ 1 } }{ 2x^2 }=\frac{ \color{purple}{ 12x^2+1 } }{ 2x^2 } \end{aligned} $$