To simplify the expression 5/6y - 1/6b - 1/6y + 2/3b - 3, we first combine like terms:

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

Therefore, the simplified expression is 2/3y + 1/3b - 3.