In order for a line to touch on the y axis it must be at a point (0, y) at any y point. So you substitue zero in for all x variables in the equation, so it would become y= (0^2-0-2)/ (0^2-16). Which then goes to y=(0-2)/(0-16). -> y= -2/-16 ->y=1/8 (answer).
The Y-intercepts are the points where the graph intersects the y-axis. Thus the x co-ordinate of those points is ZERO. If you make the value of x ZERO , in the given equation and determine the corresponding value(s) of y you should get the answer. Hope this helps. Need more help, e-mail me.