Answer:
[tex]\boxed{-432\sqrt{2} i}[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt{-2} )( 3 \sqrt{4} ) \sqrt{-3} \times ( 2 \sqrt{-3} )( 3 \sqrt{2} ) \sqrt{2}[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times \sqrt{4} \times \sqrt{-3} \times 2 \times \sqrt{-3} \times 3 \times \sqrt{2} \times \sqrt{2}[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times 2 \times \sqrt{-3} \times 2 \times \sqrt{-3} \times 3 \times 2[/tex]
[tex]2 \times \sqrt{-2} \times 3 \times 2 \times -3 \times 2 \times 3 \times 2[/tex]
[tex]-432\sqrt{2}\sqrt{-1}[/tex]
[tex]-432\sqrt{2} i[/tex]