Evaluate 4 square root of 2+2( square root of 36- square root of 8)

$4 \sqrt{2} + 2 (\sqrt{36} - \sqrt{8})$

Simplify each term.

Rewrite $36$ as $6^{2}$ .

$4 \sqrt{2} + 2 (\sqrt{6^{2}} - \sqrt{8})$

Pull terms out from under the radical, assuming positive real numbers.

$4 \sqrt{2} + 2 (6 - \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$4 \sqrt{2} + 2 (6 - \sqrt{4 (2)})$

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

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

Pull terms out from under the radical.

$4 \sqrt{2} + 2 (6 - (2 \sqrt{2}))$

Multiply $2$ by $- 1$ .

$4 \sqrt{2} + 2 (6 - 2 \sqrt{2})$

Apply the distributive property.

$4 \sqrt{2} + 2 \cdot 6 + 2 (- 2 \sqrt{2})$

Multiply $2$ by $6$ .

$4 \sqrt{2} + 12 + 2 (- 2 \sqrt{2})$

Multiply $- 2$ by $2$ .

$4 \sqrt{2} + 12 - 4 \sqrt{2}$

Simplify by adding terms.

Subtract $4 \sqrt{2}$ from $4 \sqrt{2}$ .

$0 + 12$

Add $0$ and $12$ .

$12$