To solve this equation, we will first simplify both sides of the equation.

Starting with the left side:

6/(y-1) + 2 = y

We can simplify this by first combining the fractions on the left side:

(6 + 2(y-1))/(y-1) = y

Now, simplify further:

(6 + 2y - 2)/(y-1) = y
(2y + 4)/(y-1) = y

Moving on to the right side of the equation:

y - (2y + 4 / (1-y))

Simplify the expression by distributing the negative sign:

y - 2y - 4 / (1-y)

Combine like terms:

-y - 4 / (1-y)

Now, we have:

(2y + 4) / (y-1) = y
-y - 4 / (1-y) = y

Now, let's solve this equation:

(2y + 4) / (y-1) = y

Cross multiply:

2y + 4 = y(y-1)
2y + 4 = y^2 - y

Rearrange to standard form:

y^2 - 3y - 4 = 0

Now let's solve the quadratic equation for y by factoring or using the quadratic formula.