How far from the left wall did it bounce?

A hard-level "Length" problem.For a bounce, reflect and straighten. Turning a bent path into a straight one is a powerful move.

GivenA table 12 m wide. A ball is hit from A, 3 m up the left wall, bounces once off the bottom wall, and hits B, 6 m up the right wall.

Hints

When it bounces, the angle coming in equals the angle going out. But we do not know what that angle is, so this alone will not give us a length.
Here is the move: treat the bottom wall as a mirror and reflect A across it. Call the reflected point A′ — it sits the same 3 m from the wall, but below.
Reflection keeps lengths and angles, so A′-to-bounce is exactly as long as A-to-bounce. The ball's path has simply been copied to the other side of the wall.
And here is the payoff: because the two angles are equal, A′ → bounce → B is perfectly straight. The bent path has turned into an ordinary straight line.
Now it is just similar triangles. From A′ to B the line rises 3 + 6 = 9 m while running 12 m across. The bounce happens after 3 m of that rise, so across it is 12 × 3 ÷ 9.

Answer 4m