Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrr} & 8x^2 & \\ \color{blue}{ + } & & 4x \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrr} & 8x^2 & \\ \color{blue}{ + } & & 4x \\ \hline & 8x^2 & 4x \end{array} $$