This can first of all be simplified by collecting like terms. 6x-3x=3x, so lets look at the problem as 3x-18 instead.
To find a factor, we want a value that each term can be divided evenly by. In this case, the factor is 3. If you divide each term by 3, you get x and - 6, allowing us to rewrite the expression as 3(x-6)