Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 8x^2 & 3x & 4 \\ \color{blue}{ + } & 3x^2 & 5x & 8 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 8x^2 & 3x & 4 \\ \color{blue}{ + } & 3x^2 & 5x & 8 \\ \hline & 11x^2 & 8x & 12 \end{array} $$