To solve this equation, let's first get rid of the denominators by finding a common denominator. The least common denominator for 2, 3, and 6 is 6.

So, we multiply every term by 6 to get rid of the denominators:

6((2-y)/3) - 6((6-y)/2) = 6((2-3y)/6)

Now simplify:

2(2 - y) - 3(6 - y) = 6*(2 - 3y)

4 - 2y - 18 + 3y = 12 - 18y

Combine like terms:

-14 + y = 12 - 18y

Now isolate the variable terms on one side:

y + 18y = 12 + 14

19y = 26

Finally, solve for y:

y = 26/19

Therefore, the solution to the equation is y = 26/19.