We need to factor both numerator and denominator:
`(2x^2-8)/(4x+8)=(2(x^2-4))/(4(x+2))`
At this point we can only cancel the [leading] 2 and 4:
`(2(x^2-4))/(4(x+2))=(x^2-4)/(2(x+2))`
Now, we recognize that the numerator is the difference of 2 squares:
`(x^2-4)/(2(x+2))=((x+2)(x-2))/(2(x+2)`
Now, since the terms in brackets are connected by multiplication, we can cancel the (x + 2) from top and bottom:
`((x+2)(x-2))/(2(x+2))=(x-2)/2`