Here is the equation given:
[tex]-6x=12-4y[/tex]
In the equation, you're looking for y. That means you need to move anything with the variable y to the other side.
In this equation, you have 12-4y. To move 12 to the other side, you will need to subtract 12 on both sides. This is because when a variable or integer is moved, the sign changes. The 12 was originally positive, but when moving it, it will become -12, which is why it was subtracted.
[tex]-6x-12=12-4y-12 \\-6x-12=-4y[/tex]
Remember you're looking for y alone. y is currently -4y. To remove the -4 that is being multiplied by y, you will need to do the opposite of it, which is divide by -4. Divide both sides by -4:
[tex]\frac{-6x-12}{-4} =\frac{-4y}{-4}[/tex]
When a negative number is multiplied by another negative number, the sign becomes positive. On the left side, you have -6x-12, which is being divided by -4. When you divide, [tex]\frac{-6x}{-4}[/tex] becomes [tex]\frac{6}{4}[/tex].
[tex]\frac{-6x-12}{-4} =\frac{-4y}{-4}\\\frac{6}{4}x+3=y[/tex]
[tex]\frac{6}{4}[/tex] cans till be simplified. The greatest common factor of 6 and 4 is 2, so divide the fraction by 2.
[tex]\frac{6 \div 2}{4 \div 2} =\frac{3}{2}[/tex]
That means [tex]\frac{3}{2}x+3=y[/tex]
The answer you are looking is [tex]\bf \frac{3}{2}[/tex].
