equation simplification. $(5y-1)/3 + 4 =(-8y+4)/6$ Simplification of this equation gives two answers when approched by two different methods.
Method 1 Using L.C.M( least common multiple)
$(5y-1)/3 + 4 =(-8y+4)/6$
$(5y-1+12)/3 = (-8y+4)/6$
$5y-11 =  (-8y+4)/2$
$(5y-11)2= (-8y+4)$
$10y-22 = -8y+4$
$18y=26$
$y = 26/18=13/9$
Method 2 multiplying every term by 3
$3(5y-1)/3 + 4*3 = 3(-8y+4)/6$
$5y-1 + 12 = (-8y+4)/2$
$2(5y-1 + 12) = -8y+4$
$10y-2+24  =  -8y+4$
$18y + 22 = 4$
$18y = -18$
$y = -1$
The correct method is method 2 and the correct answer is y = -1
Why is method 1 is incorrect? Could anyone explain why the answer is wrong when using the L.C.M( method 1)?

When you do two algebraic manipulations simultaneously, like here:
$$(5y-1+12)/3 = (-8y+4)/6$$
$$5y-11 = (-8y+4)/2$$
i.e. multiply through by $3$ AND simplify the left bracket, you have confusion. It should be $5y+11$. And you could always multiply through by $6$ instead of $3$ ($6=\operatorname{lcm}(3,6)$).
I would:
$$(5y-1)/3 + 4 =(-8y+4)/6$$
Multiply both sides by $6$:
$$2(5y-1)+24=-8y+4$$
Expand brackets:
$$10y-2+24=-8y+4$$
Simplify $-2+24$:
$$10y+22=-8y+4$$
Add $8y$ to both sides:
$$10y+22+8y=-8y+4+8y$$
Simplify:
$$18y+22=4$$
Add $-22$ to both sides
$$18y+22-22=4-22$$
Simplify:
$$18y=-18$$
Divide both sides by $18$:
$$y=-1$$
