$\frac{ 4\left( x+4 \right)-2\left( x-2 \right) }{ \left( x-2 \right) \times \left( x+4 \right) }$
Distribute $4$ through the parentheses$\frac{ 4x+16-2\left( x-2 \right) }{ \left( x-2 \right) \times \left( x+4 \right) }$
Distribute $-2$ through the parentheses$\frac{ 4x+16-2x+4 }{ \left( x-2 \right) \times \left( x+4 \right) }$
Simplify the expression$\frac{ 4x+16-2x+4 }{ {x}^{2}+4x-2x-8 }$
Collect like terms$\frac{ 2x+16+4 }{ {x}^{2}+4x-2x-8 }$
Add the numbers$\frac{ 2x+20 }{ {x}^{2}+4x-2x-8 }$
Collect like terms$\frac{ 2x+20 }{ {x}^{2}+2x-8 }$