The problem requires us to multiply and simplify the expression $(9\sqrt{7})(-6\sqrt{3})$.

1. Problem Description

The problem requires us to multiply and simplify the expression $(9\sqrt{7})(-6\sqrt{3})$.

2. Solution Steps

We multiply the coefficients and the radicals separately.

$(9\sqrt{7})(-6\sqrt{3}) = (9 \times -6)(\sqrt{7} \times \sqrt{3})$

$9 \times -6 = -54$

$\sqrt{7} \times \sqrt{3} = \sqrt{7 \times 3} = \sqrt{21}$

So, $(9\sqrt{7})(-6\sqrt{3}) = -54\sqrt{21}$.

3. Final Answer

-54$\sqrt{21}$