Factor the expression

1/3x - 5/6 = 1/6(?)

it's not an expression, it's an equation. If you want to solve for x, then

1/3 x = 1/6 + 5/6
1/3 x = 1
x = 3

so, what do you really want to do?

1/3x - 5/6 = 2/6x - 5/6 = 1/6 (2x-5)