The inequality is
[tex]\begin{gathered} 18(\frac{1}{3}x+6)>3(2x-6) \\ \text{divide both sides by 3} \\ 6(\frac{1}{3}x+6)>2x-6 \\ \frac{6\ast x}{3}+6\ast6>2x-6 \\ 2x+36>2x-6 \\ 2x+42>2x \\ \\ \end{gathered}[/tex][tex]\begin{gathered} 42>2x-2x \\ 42>0 \\ \end{gathered}[/tex]
42>0 IS TRUE . SO, THERE ARE INFINITE SOLUTIONS TO THE INEQUALITY.
