The problem asks us to multiply and simplify the expression $-2\sqrt{a}(\sqrt{7b}+3\sqrt{6})$. We assume that all variables represent nonnegative numbers.

1. Problem Description

The problem asks us to multiply and simplify the expression $-2\sqrt{a}(\sqrt{7b}+3\sqrt{6})$. We assume that all variables represent nonnegative numbers.

2. Solution Steps

First, distribute the $-2\sqrt{a}$ term to both terms inside the parenthesis:

$-2\sqrt{a}(\sqrt{7b}+3\sqrt{6}) = -2\sqrt{a} \cdot \sqrt{7b} - 2\sqrt{a} \cdot 3\sqrt{6}$

Next, multiply the terms. Remember that $\sqrt{x} \cdot \sqrt{y} = \sqrt{xy}$:

$-2\sqrt{a} \cdot \sqrt{7b} = -2\sqrt{7ab}$

$-2\sqrt{a} \cdot 3\sqrt{6} = -6\sqrt{6a}$

Therefore, the expression becomes:

$-2\sqrt{7ab} - 6\sqrt{6a}$

Since there are no like terms, we cannot simplify further.

3. Final Answer

$-2\sqrt{7ab} - 6\sqrt{6a}$