Answer:
3(t+2)
Step-by-step explanation:
As with any problem involving division of fractions, you can invert the denominator and multiply.
Your knowledge of the factoring of the difference of squares helps. If that doesn't work for you, you can always use synthetic division or polynomial long division to find the quotient of (t^2-4) and (t-2).
[tex]\displaystyle\frac{\frac{4t^2-16}{8}}{\frac{t-2}{6}}=\frac{4(t^2-4)}{8}\cdot\frac{6}{t-2}\\\\=\frac{3(t+2)(t-2)}{t-2}=3(t+2)[/tex]
