Given the expression:
[tex]\frac{1}{2}(12x-8)-\frac{1}{3}(18x-12)[/tex]using the distributive property we get the following:
[tex]\begin{gathered} \frac{1}{2}(12x-8)-\frac{1}{3}(18x-12)+ \\ \frac{1}{2}(12x)+\frac{1}{2}(-8)-\frac{1}{3}(18x)-\frac{1}{3}(-12)= \\ 6x-4-6x+4=0 \end{gathered}[/tex]therefore, the simplified expression is 0