One way to do it is to make a right triangle along one of the sides:
An isosceles trapezoid looks like this (by mathwords.com):
So in this case our long base is 18, short base is 12. If we draw a straight line down from the corner of the small base and one of the legs, we can get the height of the resulting triangle which will be the same as the height of the trapezoid.
We know that the long base is 6 longer than the short base, so the base of our triangle must be half of that, or 3. Thus we have a right triangle with base 3 and hypotenuse 9. We can use the pythagorean theorem to get the height.
9^2 = 3^2 - (height)^2
height = sqrt(81 - 9) = about 8.5 = altitude