Solenoid within a solenoid

I was looking at Griffiths intro to electrodynamics problem 6.12 and Im confused by the solution given in the solution manual.

If you have this book or not Ill explain the problem anyway.

We have an infinitely long cylinder that has volume current going in one direction around its axis and surface current going in the opposite direction. The solution manual describes this as like a superposition of solenoids. This leads to a non zero B field in the cylinder.

This is what I dont understand. I thought the B field in the solenoid would be zero. If there was concentric solenoids wouldnt they just cancel each other over an over again until you reached the centre?

Thanks