Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & -4x^2 & 6x & 1 \\ \color{blue}{ + } & & 5x & 7 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lrrr} & -4x^2 & 6x & 1 \\ \color{blue}{ + } & & 5x & 7 \\ \hline & -4x^2 & 11x & 8 \end{array} $$