jmc

A $y$-intercept is a point on the graph that lies on the $y$-axis, so $x=0$. Hence, the number $y$-intercepts corresponds to the number of real solutions of the quadratic equation $-y^2+4y-4$. The discriminant of this quadratic equation is $4^2-4\cdot (-1)\cdot (-4)=0$, so the quadratic has exactly one real root. (We can also see this by writing $-y^2+4y-4=-(y-2{)}^2$.) Therefore, the number of $y$-intercepts is $\boxed{1}$.