SOLUTION: What is the Least Common Denominator of 2(3+2x)= 3(x-4)?

Since there are no denominators in that equation, it 
makes no sense to ask "What is the Least Common 
Denominator of it?" 

What would make sense is to ask:  

"How do you solve for x?

2(3 + 2x) = 3(x - 4)

Distiribute to remove the parentheses:

   6 + 4x = 3x - 12

Subtract 3x from both sides:

   6 + 4x = 3x - 12
      -3x  -3x
   ----------------
   6 + 1x =  0 - 12

or

    6 + x = -12

Subtract 6 from both sides:

    6 + x = -12
   -6        -6
   ------------
    0 + x = -18

        x = -18

Edwin