(x/4)^2-(y/6)^2=1 is another way of writing the equation for the hyperbola.
The asymptotes are given by y=±6x/4=±3x/2, i.e., the lines y=3x/2 and y=-3x/2.
The vertices are where the curves cross the x axis (y=0), when x/4=±1, so x=-4 and 4, (-4,0) and (4,0).