Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & 8y^2 & 5y & 6 \\ \color{red}{ - } & & y & 1 \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & 8y^2 & 5y & 6 \\ \color{red}{ - } & & -y & -1 \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrr} & 8y^2 & 5y & 6 \\ \color{red}{ - } & & -y & -1 \\ \hline & 8y^2 & 6y & 7 \end{array} $$