Multiply, and then simplify. \[ 6(\sqrt{45}-\sqrt{20}) \]

First, let's distribute the 6 into the expression: \[ 6(\sqrt{45} - \sqrt{20}) = 6\sqrt{45} - 6\sqrt{20}. \] Next, we simplify \(\sqrt{45}\) and \(\sqrt{20}\). Starting with \(\sqrt{45}\): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}. \] Now for \(\sqrt{20}\): \[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}. \] Now, substitute these simplified forms back into the expression: \[ 6\sqrt{45} - 6\sqrt{20} = 6(3\sqrt{5}) - 6(2\sqrt{5}). \] This simplifies further: \[ 18\sqrt{5} - 12\sqrt{5} = (18 - 12)\sqrt{5} = 6\sqrt{5}. \] Thus, the final result is: \[ \boxed{6\sqrt{5}}. \]