2/3(6x - 9)?

2/3(6x - 9) = 0  (your statement)
4x - 6 = 0  (apply distributive rule)
4x - 6 + 6 = 0 + 6  (add 6)
4x = 6 (collect terms)
4x/4 = 6/4  (divide by 4)
x = 6/4  (simplify)
x = 3/2  (simplify fraction)
x = 1 1/2  (convert into improper fraction)

Alternate forms for 2/3(6x - 9):

4x - 6  (apply distributive rule)
2(2x - 3)  (factor)