The problem asks to multiply and simplify the expression $(2\sqrt{3})(-3\sqrt{5})$.

1. Problem Description

The problem asks to multiply and simplify the expression $(2\sqrt{3})(-3\sqrt{5})$.

2. Solution Steps

We multiply the numbers outside the square roots and the numbers inside the square roots.

$(2\sqrt{3})(-3\sqrt{5}) = (2 \cdot -3)(\sqrt{3} \cdot \sqrt{5})$

We have $2 \cdot -3 = -6$.

Also, $\sqrt{3} \cdot \sqrt{5} = \sqrt{3 \cdot 5} = \sqrt{15}$.

Therefore,

$(2\sqrt{3})(-3\sqrt{5}) = -6\sqrt{15}$.

3. Final Answer

-6$\sqrt{15}$