Simplify -3 square root of 6x^2*2 square root of 4x^5

$- 3 \sqrt{6 x^{2}} \cdot 2 \sqrt{4 x^{5}}$

Reorder $6$ and $x^{2}$ .

$- 3 \sqrt{x^{2} \cdot 6} \cdot (2 \sqrt{4 x^{5}})$

Pull terms out from under the radical.

$- 3 (x \sqrt{6}) \cdot (2 \sqrt{4 x^{5}})$

Rewrite $4 x^{5}$ as ${(2 x^{2})}^{2} x$ .

Rewrite $4$ as $2^{2}$ .

$- 3 x \sqrt{6} \cdot (2 \sqrt{2^{2} x^{5}})$

Factor out $x^{4}$ .

$- 3 x \sqrt{6} \cdot (2 \sqrt{2^{2} (x^{4} x)})$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$- 3 x \sqrt{6} \cdot (2 \sqrt{2^{2} ({(x^{2})}^{2} x)})$

Rewrite $2^{2} {(x^{2})}^{2}$ as ${(2 x^{2})}^{2}$ .

$- 3 x \sqrt{6} \cdot (2 \sqrt{{(2 x^{2})}^{2} x})$

Pull terms out from under the radical.

$- 3 x \sqrt{6} \cdot (2 (2 x^{2} \sqrt{x}))$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$- 3 (x^{2} x) \sqrt{6} \cdot (2 (2 \sqrt{x}))$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$- 3 (x^{2} x^{1}) \sqrt{6} \cdot (2 (2 \sqrt{x}))$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 x^{2 + 1} \sqrt{6} \cdot (2 (2 \sqrt{x}))$

Add $2$ and $1$ .

$- 3 x^{3} \sqrt{6} \cdot (2 (2 \sqrt{x}))$

Multiply $2$ by $2$ .

$- 3 x^{3} \sqrt{6} \cdot (4 \sqrt{x})$

Multiply $- 3 x^{3} \sqrt{6} (4 \sqrt{x})$ .

Multiply $4$ by $- 3$ .

$- 12 x^{3} \sqrt{6} \sqrt{x}$

Combine using the product rule for radicals.

$- 12 x^{3} \sqrt{x \cdot 6}$

Reorder factors in $- 12 x^{3} \sqrt{x \cdot 6}$ .

$- 12 x^{3} \sqrt{6 x}$