6 is possible. Just did it. Less is possible. Hitting a wall gives you a vertical impulse. That can be used.

I got it in 15 but overshot the last 2, so I'd say 13 at least is possible. But definitely not 6!

There's a trick to it

I did it in 3, but you need to hit a jump from the start over, and roll far enough to go through the arch on shot 2.

I got 12. I'm not going to tell you the secret though.