C. ![-2\sqrt{ 6}](/tpl/images/0462/4790/47e33.png)
Step-by-step explanation:
We have been given an expression. We are asked to simplify the given expression.
![2\sqrt{54}-4\sqrt{24}](/tpl/images/0462/4790/96985.png)
First of all, we will factor out perfect square under the radicals as shown below:
![2\sqrt{9\cdot 6}-4\sqrt{4\cdot 6}](/tpl/images/0462/4790/8e76e.png)
![2\sqrt{3^2\cdot 6}-4\sqrt{2^2\cdot 6}](/tpl/images/0462/4790/8bf69.png)
Factor out perfect square:
![2\cdot 3\sqrt{6}-4\cdot 2\sqrt{ 6}](/tpl/images/0462/4790/edd0b.png)
![6\sqrt{6}-8\sqrt{ 6}](/tpl/images/0462/4790/fa013.png)
Combine like terms:
![-2\sqrt{ 6}](/tpl/images/0462/4790/47e33.png)
Therefore, option C is the correct choice.