Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 4x^2 & -4x & -18 \\ \color{blue}{ + } & 4x^2 & -11x & -1 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 4x^2 & -4x & -18 \\ \color{blue}{ + } & 4x^2 & -11x & -1 \\ \hline & 8x^2 & -15x & -19 \end{array} $$