To solve this equation, we need to first simplify it by finding a common denominator:

(4/y) - 2 - (2/y) = 3 - y/(y^2 - 2y)

Now, let's combine like terms:

(4/y - 2 - 2/y) = 3 - y/(y^2 - 2y)

(2/y) = 3 - y/(y^2 - 2y)

Now, let's get rid of the denominator by multiplying both sides by y:

2 = 3y - y^2/(y^2 - 2y)

Next, let's simplify the equation by multiplying both sides by (y^2 - 2y):

2(y^2 - 2y) = 3y(y^2 - 2y) - y^2

Expand both sides:

2y^2 - 4y = 3y^3 - 6y^2 - y^2

Combine like terms:

2y^2 - 4y = 3y^3 - 7y^2

Rearrange the equation to set it equal to 0:

3y^3 - 7y^2 - 2y^2 + 4y = 0

3y^3 - 9y^2 + 4y = 0

Now, we can factor out a y:

y(3y^2 - 9y + 4) = 0

Now, solve for y using the quadratic formula:

y = (-(-9) ± √((-9)^2 - 434)) / (2*3)

y = (9 ± √(81 - 48)) / 6

y = (9 ± √33) / 6

Therefore, the solutions for y are:

y = (9 + √33) / 6 or y = (9 - √33) / 6.