$$\sqrt{18 + x \sqrt{2}} = \sqrt{12} + \sqrt{6} \Rightarrow x =$$

$$\sqrt{18 + x \sqrt{2}} = \sqrt{12} + \sqrt{6} \Rightarrow x =$$

Take square both side

$$({\sqrt{18 + x \sqrt{2}}})^2 = ({\sqrt{12} + \sqrt{6}})^2 \Rightarrow x =$$

$${18 + x \sqrt{2}} = 12 + 6 + 2 * \sqrt{12} * \sqrt{6} \Rightarrow x =$$

$${18 + x \sqrt{2}} = 18 + 2 * \sqrt{6} * \sqrt{2} * \sqrt{6} \Rightarrow x =$$

18 will be eliminated from both the sides.

$${x \sqrt{2}} = 2 * \sqrt{6} * \sqrt{2} * \sqrt{6}$$

x =2 * 6

x = 12

Hence, option C is correct.