Question 1012303
The key technique is "factor and cancel."  Here, from
{{{((2x+4)/(x^2-6x))*((x^2-36)/(4x+8))}}}
we factor and get
{{{(2(x+2)/(x(x-6))) * (((x+6)(x-6))/(4(x+2)))}}}
Now cancel and get
{{{(1/x) * ((x+6)/(2))}}} = 
{{{(x+6)/2x}}}