Answer
The intercepts with $y$ axis are $-\sqrt{2}$ and $\sqrt{2}$. The intercept with $x$ axis is $6$. The graph is symmetric with respect to $x$ axis and is shown on the figure.
Work Step by Step
To find the intercept with $y$ axis put $x=0$ and calculate $y$:
$$0+3y^2 = 6\Rightarrow 3y^2=6\Rightarrow y^2=2\Rightarrow y=\pm\sqrt{2}$$
so there are two intercepts with $y$ axis $y=-\sqrt{2}$ and $y=\sqrt{2}$.
To find the intercept with $x$ axis put $y=0$ and calculate $x$:
$$x+3\times0^2=6\Rightarrow x=6.$$
The graph is symmetric with respect to $x$ axis because if we put $-y$ instead of $y$ we obtain the same equation
$$x+3(-y)^2 = x+3y^2 = 6.$$
