Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & & 4x & -8 \\ \color{blue}{ + } & -6x^2 & 3x & \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & & 4x & -8 \\ \color{blue}{ + } & -6x^2 & 3x & \\ \hline & -6x^2 & 7x & -8 \end{array} $$