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6x=4y-3\times 2
Multiply both sides of the equation by 12, the least common multiple of 2,3,4.
6x=4y-6
Multiply -3 and 2 to get -6.
\frac{6x}{6}=\frac{4y-6}{6}
Divide both sides by 6.
x=\frac{4y-6}{6}
Dividing by 6 undoes the multiplication by 6.
x=\frac{2y}{3}-1
Divide 4y-6 by 6.