Question 107084
facrorise all components of this question first.

4x^2-16 =4(x^2-4)= 4(x-2)(x+2)       (differnce of 2 squares)
4x-24=4(x-6)
x^2-4x-12= (x-6)(x+2)

when we divide two fractions, we can flip the second one up-side-down and multiply

so we have:

{{{16x/(4(x-2)(x+2))}}} multiplied by {{{((x-6)(x+2))/(4(x-6))}}}

which is {{{(16x(x-6)(x+2))/(16(x-2)(x+2)(x-6))}}}

a lot of terms now cancel like the 16, x-6, x+2

we are left with {{{x/(x-2)}}}