$\frac{ 6{a}^{2} }{ {a}^{2}+8a+16 } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ 6a }$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression$\frac{ 6{a}^{2} }{ {\left( a+4 \right)}^{2} } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ 6a }$
Cancel out the greatest common factor $6$$\frac{ {a}^{2} }{ {\left( a+4 \right)}^{2} } \times \frac{ \left( a-4 \right) \times \left( a+4 \right) }{ a }$
Cancel out the common factor $a$$\frac{ a }{ {\left( a+4 \right)}^{2} } \times \left( a-4 \right) \times \left( a+4 \right)$
Cancel out the common factor $a+4$$\frac{ a }{ a+4 } \times \left( a-4 \right)$
Calculate the product$\frac{ {a}^{2}-4a }{ a+4 }$