The synthetic division table is:
$$ \begin{array}{c|rrrr}2&-1&-6&9&11\\& & -2& -16& \color{black}{-14} \\ \hline &\color{blue}{-1}&\color{blue}{-8}&\color{blue}{-7}&\color{orangered}{-3} \end{array} $$The solution is:
$$ \frac{ -x^{3}-6x^{2}+9x+11 }{ x-2 } = \color{blue}{-x^{2}-8x-7} \color{red}{~-~} \frac{ \color{red}{ 3 } }{ x-2 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -2 = 0 $ ( $ x = \color{blue}{ 2 } $ ) at the left.
$$ \begin{array}{c|rrrr}\color{blue}{2}&-1&-6&9&11\\& & & & \\ \hline &&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrr}2&\color{orangered}{ -1 }&-6&9&11\\& & & & \\ \hline &\color{orangered}{-1}&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 2 } \cdot \color{blue}{ \left( -1 \right) } = \color{blue}{ -2 } $.
$$ \begin{array}{c|rrrr}\color{blue}{2}&-1&-6&9&11\\& & \color{blue}{-2} & & \\ \hline &\color{blue}{-1}&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -6 } + \color{orangered}{ \left( -2 \right) } = \color{orangered}{ -8 } $
$$ \begin{array}{c|rrrr}2&-1&\color{orangered}{ -6 }&9&11\\& & \color{orangered}{-2} & & \\ \hline &-1&\color{orangered}{-8}&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 2 } \cdot \color{blue}{ \left( -8 \right) } = \color{blue}{ -16 } $.
$$ \begin{array}{c|rrrr}\color{blue}{2}&-1&-6&9&11\\& & -2& \color{blue}{-16} & \\ \hline &-1&\color{blue}{-8}&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ 9 } + \color{orangered}{ \left( -16 \right) } = \color{orangered}{ -7 } $
$$ \begin{array}{c|rrrr}2&-1&-6&\color{orangered}{ 9 }&11\\& & -2& \color{orangered}{-16} & \\ \hline &-1&-8&\color{orangered}{-7}& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 2 } \cdot \color{blue}{ \left( -7 \right) } = \color{blue}{ -14 } $.
$$ \begin{array}{c|rrrr}\color{blue}{2}&-1&-6&9&11\\& & -2& -16& \color{blue}{-14} \\ \hline &-1&-8&\color{blue}{-7}& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 11 } + \color{orangered}{ \left( -14 \right) } = \color{orangered}{ -3 } $
$$ \begin{array}{c|rrrr}2&-1&-6&9&\color{orangered}{ 11 }\\& & -2& -16& \color{orangered}{-14} \\ \hline &\color{blue}{-1}&\color{blue}{-8}&\color{blue}{-7}&\color{orangered}{-3} \end{array} $$Bottom line represents the quotient $ \color{blue}{ -x^{2}-8x-7 } $ with a remainder of $ \color{red}{ -3 } $.