The best way to do this problem (and others like it) is as follows:
1: multiply (distribute) everything out
2: group terms with the variable you want together
3: factor and solve
2ab = 3b (2b - 3a)... multiply
2ab = 6b^2 - 9ab... group things together
2ab + 9ab = 6b^2
11ab = 6b^2... now divide to solve for a
a = 6b^2 / (11b)
a = (6/11)b
1: multiply (distribute) everything out
2: group terms with the variable you want together
3: factor and solve
2ab = 3b (2b - 3a)... multiply
2ab = 6b^2 - 9ab... group things together
2ab + 9ab = 6b^2
11ab = 6b^2... now divide to solve for a
a = 6b^2 / (11b)
a = (6/11)b