$\frac{ {x}^{2}+6x+2x+12 }{ {x}^{2}+12x+36 } \times \frac{ {x}^{2}+6x }{ {x}^{2}+\left( 4x \right)+4 }$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression$\frac{ {x}^{2}+6x+2x+12 }{ {\left( x+6 \right)}^{2} } \times \frac{ {x}^{2}+6x }{ {x}^{2}+\left( 4x \right)+4 }$
Factor out $x$ from the expression$\frac{ {x}^{2}+6x+2x+12 }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {x}^{2}+\left( 4x \right)+4 }$
When there is a $+$ in front of an expression in parentheses, the expression remains the same$\frac{ {x}^{2}+6x+2x+12 }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {x}^{2}+4x+4 }$
Factor out $x$ from the expression$\frac{ x \times \left( x+6 \right)+2x+12 }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {x}^{2}+4x+4 }$
Factor out $2$ from the expression$\frac{ x \times \left( x+6 \right)+2\left( x+6 \right) }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {x}^{2}+4x+4 }$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression$\frac{ x \times \left( x+6 \right)+2\left( x+6 \right) }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {\left( x+2 \right)}^{2} }$
Factor out $x+6$ from the expression$\frac{ \left( x+6 \right) \times \left( x+2 \right) }{ {\left( x+6 \right)}^{2} } \times \frac{ x \times \left( x+6 \right) }{ {\left( x+2 \right)}^{2} }$
Cancel out the common factor $x+6$$\frac{ x+2 }{ x+6 } \times \frac{ x \times \left( x+6 \right) }{ {\left( x+2 \right)}^{2} }$
Cancel out the common factor $x+2$$\frac{ 1 }{ x+6 } \times \frac{ x \times \left( x+6 \right) }{ x+2 }$
Cancel out the common factor $x+6$$1 \times \frac{ x }{ x+2 }$
Any expression multiplied by $1$ remains the same$\frac{ x }{ x+2 }$