[tex]\begin{gathered} \text{From the figure} \\ \text{hypotenuse}=4\sqrt[]{2} \\ \text{opposite to angle 60=y} \\ \text{adjacent to angle 60 = x} \\ \\ \cos \text{ 60 = }\frac{\text{adjacent}}{\text{Hypotenuse}} \\ \cos \text{ 60=}\frac{x}{4\sqrt[]{2}} \\ \\ x=4\sqrt[]{2}\text{ cos 60} \\ x=4\sqrt[]{2}\text{ x }\frac{1}{2} \\ x=2\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} \sin \text{ 60=}\frac{opposite}{\text{hypotenuse}} \\ \\ \sin \text{ 60= }\frac{y}{4\sqrt[]{2}} \\ \\ y=4\sqrt[]{2}\text{ x sin60} \\ y=4\sqrt[]{2}\text{ x}\frac{\sqrt[]{3}}{2} \\ \\ y=2\sqrt[]{6} \end{gathered}[/tex]
The correct option is option C
