How do you simplify  6sqrt2divsqrt3?

The answer is $2 \sqrt{6}$
You can do this simplification by "rationalizing the denominator". That is, multiply $\frac{6 \sqrt{2}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$. Doing this gives $\frac{6 \sqrt{6}}{3} = 2 \sqrt{6}$
I used the fact that $\sqrt{2} \sqrt{3} = \sqrt{6}$ in this simplification.