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\left(x-2\right)\times 3-x\times 2=0
Variable x cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by x\left(x-2\right), the least common multiple of x,x-2.
3x-6-x\times 2=0
Use the distributive property to multiply x-2 by 3.
3x-x\times 2=6
Add 6 to both sides. Anything plus zero gives itself.
3x-2x=6
Multiply -1 and 2 to get -2.
x=6
Combine 3x and -2x to get x.