It is really simple if you know the trick. The trick is understanding that whatever you do equally to the top and bottom of a fraction does not change it.
Example: 5/7 I can multiply the top and bottom by 3 and nothing changes
15/21 = 5/7
So you use the same concept to clear the fractions. In your example you have
-6 / (2/3)
Multiply the bottom by 3 and top by 3 to make the bottom part a whole number.
-6 * 3 / (2/3)*3 = -18 / 2
Now simplify: -18/2 = -9
In more advanced math, like algebra, you will use this concept all the time, but instead of top / bottom, you can do anything as long as you do it to both sides of the equals sign. Very powerful concept that will take you far in math.