Express your solution as an integer, a simplified fraction, or a de \[ \frac{1}{6} y-\frac{1}{3}=-\frac{3}{2} y+\frac{5}{6} \]

Let's solve the equation step by step. We start with: \[ \frac{1}{6} y - \frac{1}{3} = -\frac{3}{2} y + \frac{5}{6} \] First, we can eliminate the fractions by finding a common denominator, which is 6: \[ \frac{1}{6} y - \frac{2}{6} = -\frac{9}{6} y + \frac{5}{6} \] Next, multiply each term by 6 to clear the denominators: \[ 1y - 2 = -9y + 5 \] Now, let's rearrange the equation by adding \(9y\) to both sides and adding \(2\) to both sides: \[ 1y + 9y = 5 + 2 \] \[ 10y = 7 \] Now, divide both sides by 10 to solve for \(y\): \[ y = \frac{7}{10} \] Thus, the solution is: \[ y = \frac{7}{10} \] as a simplified fraction.