The problem asks us to multiply and simplify the expression $(3\sqrt{2})(-4\sqrt{3})$.

1. Problem Description

The problem asks us to multiply and simplify the expression $(3\sqrt{2})(-4\sqrt{3})$.

2. Solution Steps

First, we multiply the numbers outside the square roots: $3 \cdot (-4) = -12$.

Then, we multiply the numbers inside the square roots: $\sqrt{2} \cdot \sqrt{3} = \sqrt{2 \cdot 3} = \sqrt{6}$.

Combining these results, we get $-12\sqrt{6}$.

3. Final Answer

$-12\sqrt{6}$