Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrrr} & -9x^4 & 19x^2 & -8x & -12 \\ \color{blue}{ + } & & & -6x & \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrrr} & -9x^4 & 19x^2 & -8x & -12 \\ \color{blue}{ + } & & & -6x & \\ \hline & -9x^4 & 19x^2 & -14x & -12 \end{array} $$