How can you eliminate fraction from each side of the equation to make finding the solution easier 1/2(x-4)=1/3x+2

Multiply by the product of the denominators. Here, that is 2*3 = 6.

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The above approach always works. You likely have been told to multiply by the least common denominator, which in this case is the same thing.

If you don't take the trouble to find the least common denominator, at some point you will be factoring out a common factor. (You may be doing that anyway.)

1/2(x-4)=1/3x+2
3(x -4) = 2x +12
x = 24