Introduction:
In this problem, we are given the magnitudes of four vectors a, b, c, d and the magnitude of the net resultant force. We are required to find the maximum and minimum magnitude of the four vectors.

Method:
To find the maximum and minimum magnitudes of the four vectors, we can use the triangle inequality. The triangle inequality states that the magnitude of the sum of two vectors is always less than or equal to the sum of the magnitudes of the individual vectors.

Calculation:
Let's first find the minimum value of x.
Using the triangle inequality for vectors a, b, and c, we get:
|a + b + c| ≤ |a| + |b| + |c|
2 + 8 + 6 ≤ 20
We know that the magnitude of the net force is 20, so the above inequality holds true.
Now, let's use the triangle inequality for vectors a, b, c, and d:
|a + b + c + d| ≤ |a| + |b| + |c| + |d|
2 + 8 + 6 + x ≤ 20
Solving for x, we get:
x ≤ 4

Therefore, the minimum value of x is 4.

Now, let's find the maximum value of x.
Using the triangle inequality for vectors a, b, c, and d, we get:
|a + b + c + d| ≤ |a| + |b| + |c| + |d|
2 + 8 + 6 + x ≤ 2 + 8 + 6 + 20
Solving for x, we get:
x ≤ 16

Therefore, the maximum value of x is 16.

Conclusion:
We have found that the minimum magnitude of vector d is 4 and the maximum magnitude of vector d is 16. The triangle inequality provides a useful tool for finding the maximum and minimum magnitudes of vectors.

The magnitude of the fourth force