Answer
Elliptic paraboloid.
Work Step by Step
The equation can be rewritten in the form
$$
z= \left(\frac{x}{3\sqrt{2}}\right)^{2}+\left(\frac{y}{4\sqrt{2}}\right)^{2}
$$
which is an elliptic paraboloid.
(See equations on page 691-692.)
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