The synthetic division table is:
$$ \begin{array}{c|rrrrr}-4&1&-4&-20&32&73\\& & -4& 32& -48& \color{black}{64} \\ \hline &\color{blue}{1}&\color{blue}{-8}&\color{blue}{12}&\color{blue}{-16}&\color{orangered}{137} \end{array} $$The solution is:
$$ \frac{ x^{4}-4x^{3}-20x^{2}+32x+73 }{ x+4 } = \color{blue}{x^{3}-8x^{2}+12x-16} ~+~ \frac{ \color{red}{ 137 } }{ x+4 } $$Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x + 4 = 0 $ ( $ x = \color{blue}{ -4 } $ ) at the left.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&1&-4&-20&32&73\\& & & & & \\ \hline &&&&& \end{array} $$Step 1 : Bring down the leading coefficient to the bottom row.
$$ \begin{array}{c|rrrrr}-4&\color{orangered}{ 1 }&-4&-20&32&73\\& & & & & \\ \hline &\color{orangered}{1}&&&& \end{array} $$Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 1 } = \color{blue}{ -4 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&1&-4&-20&32&73\\& & \color{blue}{-4} & & & \\ \hline &\color{blue}{1}&&&& \end{array} $$Step 3 : Add down last column: $ \color{orangered}{ -4 } + \color{orangered}{ \left( -4 \right) } = \color{orangered}{ -8 } $
$$ \begin{array}{c|rrrrr}-4&1&\color{orangered}{ -4 }&-20&32&73\\& & \color{orangered}{-4} & & & \\ \hline &1&\color{orangered}{-8}&&& \end{array} $$Step 4 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ \left( -8 \right) } = \color{blue}{ 32 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&1&-4&-20&32&73\\& & -4& \color{blue}{32} & & \\ \hline &1&\color{blue}{-8}&&& \end{array} $$Step 5 : Add down last column: $ \color{orangered}{ -20 } + \color{orangered}{ 32 } = \color{orangered}{ 12 } $
$$ \begin{array}{c|rrrrr}-4&1&-4&\color{orangered}{ -20 }&32&73\\& & -4& \color{orangered}{32} & & \\ \hline &1&-8&\color{orangered}{12}&& \end{array} $$Step 6 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ 12 } = \color{blue}{ -48 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&1&-4&-20&32&73\\& & -4& 32& \color{blue}{-48} & \\ \hline &1&-8&\color{blue}{12}&& \end{array} $$Step 7 : Add down last column: $ \color{orangered}{ 32 } + \color{orangered}{ \left( -48 \right) } = \color{orangered}{ -16 } $
$$ \begin{array}{c|rrrrr}-4&1&-4&-20&\color{orangered}{ 32 }&73\\& & -4& 32& \color{orangered}{-48} & \\ \hline &1&-8&12&\color{orangered}{-16}& \end{array} $$Step 8 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ -4 } \cdot \color{blue}{ \left( -16 \right) } = \color{blue}{ 64 } $.
$$ \begin{array}{c|rrrrr}\color{blue}{-4}&1&-4&-20&32&73\\& & -4& 32& -48& \color{blue}{64} \\ \hline &1&-8&12&\color{blue}{-16}& \end{array} $$Step 9 : Add down last column: $ \color{orangered}{ 73 } + \color{orangered}{ 64 } = \color{orangered}{ 137 } $
$$ \begin{array}{c|rrrrr}-4&1&-4&-20&32&\color{orangered}{ 73 }\\& & -4& 32& -48& \color{orangered}{64} \\ \hline &\color{blue}{1}&\color{blue}{-8}&\color{blue}{12}&\color{blue}{-16}&\color{orangered}{137} \end{array} $$Bottom line represents the quotient $ \color{blue}{ x^{3}-8x^{2}+12x-16 } $ with a remainder of $ \color{red}{ 137 } $.