To solve this equation, we'll first multiply through by 8 to get rid of the fractions:

5/12y + 3 + 2/9 + 1 + 7/8y = 5 + 1/8
40/12y + 27/9 + 8/9 + 8/8y = 40 + 1

Next, we'll simplify the equation:

10/3y + 3 + 1 + 7/8y = 41

Now, we'll consolidate the variables:

10/3y + 7/8y = 41 - 3 - 1

Now we'll simplify the equation further:

80/24y + 9/24y = 37

Now we'll combine like terms:

$80+9$/24y = 37
89/24y = 37

Finally, we'll solve for y:

y = 37 * 24 / 89
y = 10

Therefore, the solution to the equation is y = 10.