4y - 2(y - 3) - 3(y - 3(4 - 2y) + 8)

First, distribute the -2 and -3:

4y - 2y + 6 - 3y + 9(4 - 2y) + 24

Combine like terms:

4y - 2y - 3y + 9(4 - 2y) + 30

Combine the y terms:

-y + 9(4 - 2y) + 30

Distribute the 9:

-y + 36 - 18y + 30

Combine like terms:

-19y + 66

Therefore, the simplified expression is -19y + 66.