Introduction:
Arithmetic mean, also known as the average, is a measure of central tendency. It is calculated by summing up a set of numbers and dividing the sum by the count of those numbers. In this case, we are given two numbers -6 and 14, and we need to find the two arithmetic means between them.

Step 1: Finding the difference between the given numbers:
To find the arithmetic means, we first need to find the difference between the given numbers. In this case, the difference between -6 and 14 is 14 - (-6) = 20.

Step 2: Dividing the difference by the count of means:
Since we need to find two arithmetic means, we divide the difference (20) by the count of means (3). This gives us 20/3 = 6.6667.

Step 3: Finding the first arithmetic mean:
To find the first arithmetic mean, we add the divided difference (6.6667) to the smaller number (-6). This gives us -6 + 6.6667 = 0.6667.

Step 4: Finding the second arithmetic mean:
To find the second arithmetic mean, we add the divided difference (6.6667) to the first arithmetic mean (0.6667). This gives us 0.6667 + 6.6667 = 7.3334.

Summary:
The two arithmetic means between -6 and 14 are 0.6667 and 7.3334. These values divide the given range into three equal parts, with each part having a length of approximately 6.6667.

Explanation:
- In arithmetic progression, the difference between consecutive terms is constant. In this case, the difference between -6 and 14 is 20.
- To find the arithmetic means, we divide the difference by the count of means. Since we need two means, we divide 20 by 3, resulting in 6.6667.
- We then add the divided difference to the smaller number (-6) to find the first arithmetic mean. This gives us 0.6667.
- Finally, we add the divided difference to the first arithmetic mean to find the second arithmetic mean. This gives us 7.3334.
- Therefore, the two arithmetic means between -6 and 14 are 0.6667 and 7.3334.
- These means divide the given range into three equal parts, with each part having a length of approximately 6.6667.