To solve the equation Y - 4 5/6 = 2 1/6 + 5/6, we need to first convert the mixed numbers into improper fractions.

4 5/6 can be written as (6 * 4 + 5) / 6 = 29/6.

2 1/6 can be written as (6 * 2 + 1) / 6 = 13/6.

Now the equation becomes Y - 29/6 = 13/6 + 5/6.

Combining the fractions on the right side, we get Y - 29/6 = 18/6.

To eliminate the fractions, we can multiply both sides of the equation by 6:

6(Y - 29/6) = 6(18/6).

This simplifies to 6Y - 29 = 18.

Now, we can isolate Y by adding 29 to both sides:

6Y - 29 + 29 = 18 + 29.

This simplifies to 6Y = 47.

Finally, we divide both sides by 6 to solve for Y:

6Y/6 = 47/6.

Y = 47/6, which can also be written as 7 5/6.