Solve for y 4x-2y=12x

$4 x - 2 y = 12 x$

Move all terms not containing $y$ to the right side of the equation.

Subtract $4 x$ from both sides of the equation.

$- 2 y = 12 x - 4 x$

Subtract $4 x$ from $12 x$ .

$- 2 y = 8 x$

Divide each term in $- 2 y = 8 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 8 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{8 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{8 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{8 x}{- 2}$

Simplify the right side.

Cancel the common factor of $8$ and $- 2$ .

Factor $2$ out of $8 x$ .

$y = \frac{2 (4 x)}{- 2}$

Move the negative one from the denominator of $\frac{4 x}{- 1}$ .

$y = - 1 \cdot (4 x)$

Simplify the expression.

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

$y = - (4 x)$

Multiply $4$ by $- 1$ .

$y = - 4 x$