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

Starting with the given equation:

3y + 9/5 + 5y - 5/4 = 6 + 3y + 1/2

Combine the y terms:

8y + 9/5 - 5/4 = 6 + 3y + 1/2

Find a common denominator to combine the fractions on both sides:

8y + 36/20 - 25/20 = 12 + 60y + 10/20

Combine the fractions:

8y + 11/20 = 12 + 60y + 1/2

Now, isolate the variable y by moving all terms with y to one side and all constants to the other side:

8y - 60y = 12 - 11/20 - 1/2

-52y = 24 - 11/20 - 10/20

-52y = 24 - 21/20

-52y = 479/20

Divide by -52 on both sides to solve for y:

y = -479/1040

Therefore, the solution to the equation is y = -479/1040.