Answer
It is an ellipse.
See Graph I for the graphing of the equation.
Work Step by Step
For $18x^2 + 8y^2 = 72$, it can be rewritten as
$\frac{18x^2}{72} + \frac{8y^2}{72} = \frac{72}{72}$
$\frac{x^2}{4} + \frac{y^2}{9} = 1$
$\frac{x^2}{2^2} + \frac{y^2}{3^3} = 1$
It is in the form of an ellipse with center at (0, 0) and $x-intercepts$ at $\pm2$ and $y-intercept$ at $\pm3$.
See Graph I for the graphing of the equation.