To solve for y, we can start by simplifying the equation:

7(y-6)/4 = 5(y+1)/3 - 3(y+2)

First, we can distribute the constants:

(7y - 42)/4 = (5y + 5)/3 - (3y + 6)

Next, we can simplify the fractions by finding a common denominator. In this case, the common denominator is 4*3 = 12:

3(7y - 42)/12 = 4(5y + 5)/12 - 4(3y + 6)/12

Simplifying further:

21y - 126 = 20y + 20 - 12y - 24

Combine like terms:

21y - 126 = 20y + 20 - 12y - 24
21y - 126 = 8y - 4

Now, isolate y on one side:

21y - 126 = 8y - 4
21y - 8y = 126 - 4
13y = 122
y = 122/13
y = 9.38

Therefore, the value of y that satisfies the equation is y = 9.38.