To solve this equation, we need to combine like terms and isolate the variable y.

First, let's combine the terms with y:

8/15y - 3/10y = 8/15y - 0.3y = 0.5y

Now, let's rewrite the equation with the combined terms:

0.5y + 0.78 = 1.2

Next, let's isolate the variable y by moving the constant term to the other side of the equation:

0.5y = 1.2 - 0.78
0.5y = 0.42

Finally, solve for y by dividing both sides by 0.5:

y = 0.42 / 0.5
y = 0.84

Therefore, the solution to the equation is y = 0.84.