When y=0, x=+2. So the x intercepts are 2 and -2.
When x=0 y is not defined. So there are no y intercepts. Between x=-2 and 2 the curve does not exist.
There are 4 asymptotes because there is a parabolic curve on each side of the y axis cutting the x axis at -2 and 2.
We can work out the equations of the sloping asymptotes.
(x^2/4)-(y^2/9)=1, so y^2=9(x^2/4-1), y=+(3/2)sqrt(x^2-4).
Differentiating: x/2-(2/9)ydy/dx=0; x/2=+(2/9)(3/2)sqrt(x^2-4)dy/dx=+(1/3)sqrt(x^2-4)dy/dx;
dy/dx=+3x/2sqrt(x^2-4). When x is large positive or negative, dy/dx, the gradient,=+3/2. Therefore the gradients of the asymptotes are 3/2 and -3/2. The equations are y=3x/2 and y=-3x/2. They can be segmented into 4 sections to cover the curves for x<-2 and x>2.