This does not make sense to me...I come up with different answers.
4 3 2
6t - 3t - 9t
4 3 2
4t -12t + 9t
Is this what you've tried to write?
$\displaystyle \frac{6t^4 - 3t^3 - 9t^2}{4t^4 - 12t^3 + 9t^2}$?
If so, start by taking out common factors.
$\displaystyle =\frac{3t^2(2t^2 - t - 3)}{t^2(4t^2 - 12t + 9)}$
$\displaystyle =\frac{3(2t^2 - t - 3)}{4t^2 - 12t + 9}$
Now try factorising the top and the bottom.
$\displaystyle = \frac{3(2t^2 - 3t + 2t - 3)}{4t^2 - 6t - 6t + 9}$
$\displaystyle = \frac{3[t(2t - 3) + 1(2t - 3)}{2t(2t - 3) - 3(2t - 3)}$
$\displaystyle = \frac{3(t + 1)(2t - 3)}{(2t - 3)(2t - 3)}$
$\displaystyle = \frac{3(t + 1)}{2t - 3}$.
Is this the answer you were given?