Step-by-step explanation:
[tex]6\sqrt3\cdot\dfrac{\sqrt3}{3}=\dfrac{(6\sqrt3)(\sqrt3)}{3}\\\\\text{use the associative property}\ (a\times b)\times c=a\times(b\times c)\\\\=\dfrac{(6)(\sqrt3\cdot\sqrt3)}{3}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\\\\=\dfrac{(6)(\not3)}{\not3}\qquad\text{cancel 3}\\\\=6[/tex]