**Problem Analysis**

In this problem, a body is projected up an inclined plane with a certain velocity. We are given the weight of the body, the angle of inclination, and the coefficient of friction. We need to find the maximum distance the body will move up the incline and the velocity of the body when it returns to its original position.

**Solution**

To solve this problem, we will use the principles of Newtonian mechanics and the laws of motion.

**Step 1: Resolving Forces**

We start by resolving the weight of the body into two components: one parallel to the incline and one perpendicular to the incline.

The weight of the body is given as 20N. The component parallel to the incline is given by:

F_parallel = m * g * sin(theta)

where m is the mass of the body, g is the acceleration due to gravity, and theta is the angle of inclination.

The component perpendicular to the incline is given by:

F_perpendicular = m * g * cos(theta)

**Step 2: Frictional Force**

The frictional force acting on the body can be calculated using the coefficient of friction and the normal force. The normal force is given by:

N = m * g * cos(theta)

The frictional force is then given by:

F_friction = coefficient of friction * N

**Step 3: Net Force**

The net force acting on the body can be calculated by subtracting the frictional force from the component parallel to the incline:

F_net = F_parallel - F_friction

**Step 4: Acceleration**

The acceleration of the body along the incline can be calculated using Newton's second law of motion:

F_net = m * a

where a is the acceleration of the body.

**Step 5: Maximum Distance**

To find the maximum distance that the body will move up the incline, we can use the kinematic equation:

v^2 = u^2 + 2 * a * s

where v is the final velocity of the body, u is the initial velocity of the body, a is the acceleration of the body, and s is the distance traveled by the body.

At the maximum distance, the final velocity of the body will be zero. Therefore, we can rearrange the equation to solve for the distance traveled:

s = (v^2 - u^2) / (2 * a)

Substituting the given values, we can find the maximum distance.

**Step 6: Velocity at Original Position**

To find the velocity of the body when it returns to its original position, we need to consider the motion of the body along the incline and back down the incline.

Since the body is projected up the incline, its initial velocity is 12 m/s. When it reaches the maximum distance, its velocity becomes zero. As the body moves back down the incline, it will experience the same net force acting in the opposite direction. Therefore, the body will have the same acceleration as before.

Using the kinematic equation again, we can find the final velocity of the body when it returns to its original position.

**Summary**

In summary, we can find the maximum distance that the body will move up the incline by using the kinematic equation, and we can find the velocity of the body when it returns to its original position by considering the motion along the incline and back down the incline