Answer
There are no intercepts with $y$ axis. The intercept with $x$ axis is in $8/3$. 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 $y$:
$$3\times0 - 4y^2=8\Rightarrow -4y^2=8\Rightarrow y^2 = -2.$$
The last equation does not have any real solutions because no real number can be squared to yield a negative number so there are no intercepts with $y$ axis.
To find the intercept with $x$ axis put $y=0$ and calculate $x$
$$3x-40^2=8\Rightarrow 3x=8\Rightarrow x=\frac{8}{3}.$$
The graph is symmetric with respect to $x$ axis since if we put $-y$ instead of $y$ we obtain the same equation
$$3x-4(-y)^2 = 3x-4y^2 = 8$$
