Our equation is 2(y+1)-4(y-3)=6y+14-8y and our goal is to get y on one side and not y on the other.
2 (y+1) - 4 (y - 3) = 6y + 14 - 8y
2y + 2 - 4y + 12 = 6y + 14 - 8y <-- apply distribution on the left side to both pairs
-2y + 14 = 6y + 14 - 8y <--- simplify the left side and collect like terms
-2y + 14 = -2y + 14 <--- simplify the right side
-2y = -2y <--- subtract 14 on both sides
y = y <----- divide both sides by -2
We have that y is equal to y, a statement that's always true.
Thus the equation is an identity and is true for all values of y.
