Answer
$$2\left(3t^2-4t+1\right)$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{18t^3-24t^2+6t}{3t} \\ \frac{6t\left(3t^2-4t+1\right)}{3t} \\ 2\left(3t^2-4t+1\right) $$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.