**Given information:**
- Inclination of the wedge: 45°
- Acceleration of the wedge: 2√6 m/s²

**To find:**
Magnitude of acceleration of the ball placed between an inclined wall and the end wedge.

**Solution:**
1. Let's consider the inclined wall and the end wedge as a single system.
2. The acceleration of the ball can be determined by analyzing the forces acting on it.
3. There are two forces acting on the ball: gravitational force (mg) and the normal force (N).
4. The gravitational force can be resolved into two components: one perpendicular to the inclined wall (mgcosθ) and the other parallel to the inclined wall (mgsinθ).
5. The normal force (N) is perpendicular to the inclined wall and acts in the opposite direction to the gravitational force component perpendicular to the wall (mgcosθ).
6. The net force acting on the ball in the direction parallel to the inclined wall is the difference between the gravitational force component parallel to the wall (mgsinθ) and the frictional force (f).
7. The frictional force (f) can be determined using the equation f = μN, where μ is the coefficient of friction.
8. The acceleration of the ball can be determined using Newton's second law: F = ma, where F is the net force acting on the ball.
9. Since the wedge is accelerating towards the right, the net force acting on the ball will be towards the right.
10. The magnitude of the acceleration of the ball can be determined by dividing the net force acting on the ball by its mass.

**Final Answer:**
The magnitude of the acceleration of the ball placed between an inclined wall and the end wedge can be determined by analyzing the forces acting on it and applying Newton's second law. The acceleration will depend on the angle of inclination, the coefficient of friction, and the mass of the ball.