To solve the equation, we first need to simplify both sides of the equation.

(12у - 9) 4/3 = 0.5 2у
(4(12у - 9))/3 = 1 * 2у
(48у - 36)/3 = 2у
16у - 12 = 2у

Now, we need to isolate the variable y by moving all terms with y to one side of the equation:

16у - 12 = 2у
16у - 2у = 12
14у = 12

Finally, we solve for y by dividing both sides by 14:

y = 12/14
y = 6/7

Therefore, the solution to the equation is y = 6/7.