Solve the Problem $2 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 12$

Multiple Choice

Solve the problem.
-A rectangular box is to be inscribed inside the ellipsoid $2 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 12$ . Find the largest possible volume for the box.

A) $16 \sqrt { 2 }$
B) $15 \sqrt { 2 }$
C) $12 \sqrt { 2 }$
D) $18 \sqrt { 2 }$