WE have to simplify [(4t^2-16) / 8] / [(t-2) / 6]

[(4t^2-16) / 8] / [(t-2) / 6]

=> [(4t^2-16) / 8] * [6 / (t-2)]

=> [(4t^2-16)*6 / 8*(t-2)]

=> [(2t - 4)(2t + 4)*6 / 8*(t-2)]

=>[4(t - 2)(t + 2)*6 / 8*(t-2)]

=> [(t - 2)(t + 2)*3 / (t-2)]

=> [(t + 2)*3 ]

=> 3t + 6

**Therefore [(4t^2-16) / 8] / [(t-2) / 6] = 3t + 6**

To simplify 4t^2-16/8/t -6.

4t^2- 2/t - 6.

The secod term 16/2/t is treated as (16/8)/t = 8/t, as there are two divisions with out brackets. Divisions are of equal priority. Therefore 16/2 is the first division. So the priority is for 16/2.

Therefore 4t^2 -16/8/t - 6 = 4t^2-8/t - 6 which is in the simplest form.

First, we'll re-write the term 16/8/t, the denominator 8 coming down near the denominator t:

16/8/t = 16/8t

We'll divide by 8 both numerator and denominator:

16/8t = 2/t

Now, we'll simplify by 2 the term 2/6:

2/6 = 1/3

We'll re-write the given expression in a simplified manner:

4t^2 - 2/t - 1/3