To solve this equation, we first distribute the 0.8 on the left side and the 5/3 on the right side:

6.4y - 1.6 = 5y + 5/3

Next, we want to isolate the y terms. Let's subtract 5y from both sides:

6.4y - 5y - 1.6 = 5/3

1.4y - 1.6 = 5/3

Now, let's add 1.6 to both sides:

1.4y = 5/3 + 1.6
1.4y = 1.6667 + 1.6
1.4y = 3.2667

Lastly, divide by 1.4 to solve for y:

y = 3.2667 / 1.4
y = 2.3333

Therefore, the solution to the equation (8y - 2)0.8 = (3y + 1)5/3 is y = 2.3333.