How do you solve this radical problem?

You are given...

2√2·√12

Multiply...

2√24

Expand terms inside radical to get a perfect square...

2√(4·6)

Square root 4 and put it outside...

2·2√6

Multiply...

4√6

Done.

$2\times\sqrt{2}\times(-\sqrt{12})$

Since $\sqrt{2}$ and $\sqrt{12}$ are not perfect squares, instead of finding what $\sqrt{2}$  and $\sqrt{12}$ are, expand the terms inside the radicals to find perfect squares:

$2\times\sqrt{2}\times\sqrt{12}$

$2\times\sqrt{2}\times\sqrt{4\times3}$

$2\times\sqrt{2}\times\sqrt{2\times\times2\times3}$

$2\times\sqrt{2}\times2\times\sqrt{3}$

$2\times\sqrt{2}\times2\times\sqrt{3}$

$4\times\sqrt{2}\times\sqrt{3}$

$4\times\sqrt{6}$

$4\sqrt{6}$

If you want an approximate answer:

$2\times\sqrt{2}\times\sqrt{12}$

$2\times 1.414213562373095\times\sqrt{12}$

$2.82842712474619\times\sqrt{12}$

$2.82842712474619\times3.4641016151377546$

$9.797958971132712091295411504974$