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

1. Problem Description

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

2. Solution Steps

We are asked to multiply $(3\sqrt{2})(-4\sqrt{3})$. We can rearrange the terms as:

$(3)(-4)(\sqrt{2})(\sqrt{3})$

Multiplying the constants $3$ and $-4$ yields $-12$.

Multiplying the square roots, we have

$\sqrt{2}\sqrt{3} = \sqrt{2 \times 3} = \sqrt{6}$.

Thus, we have

$-12\sqrt{6}$.

3. Final Answer

$-12\sqrt{6}$