Answer
When the ball reaches the bottom of the stairs, it still bounces back up $3m$ in height.
Work Step by Step
We take a look at each bounce: the initial point is just before the bounce, when $v_0=0$, and the final point is the highest point the ball can bounce back, when $v_f=0$
Since all the collisions are elastic, no kinetic energy is lost to the step, and since air resistance is neglected, we apply mechanical energy conservation: $$mg(h_f-h_0)=\frac{1}{2}m(v_f^2-v_0^2)=\frac{1}{2}m(0-0)=0$$ $$h_f=h_0$$
This means after each bounce, the ball rises up to the original height before the bounce. Therefore, when the ball reaches the bottom of the stairs, it still bounces back up $3m$ in height.
