To solve this equation, we first need to combine like terms on both sides.

Starting with the left side of the equation:

7у - 4/9 - 8 - 2у/6

Combine the у terms:

7у - 2у = 5у

Combine the constants:

-4/9 - 8 = -77/9

Now the left side becomes:

5у - 77/9 - 2у/6

To make the terms easier to combine, convert 2у/6 to у/3:

5у - 77/9 - у/3

Now let's simplify the right side of the equation:

3у + 3/4

Now the equation looks like this:

5у - 77/9 - у/3 = 3у + 3/4

To solve for у, we need to combine the у terms on one side of the equation and the constant terms on the other side. Let's start by moving all the terms involving у to the left side:

5у - у/3 - 3у = 77/9 + 3/4

Now combine the у terms:

5у - у/3 - 3у = 4у - у/3

Combine the constant terms:

77/9 + 3/4 = 341/36

Now our equation looks like this:

4у - у/3 = 341/36

To simplify this further, we can multiply everything by 3 to get rid of the fraction:

12у - у = 113

Now combine the у terms:

11у = 113

Divide by 11 to solve for у:

у = 113/11

Therefore, у = 10.272727272727273