Arithmetic Mean:
Arithmetic mean is defined as the sum of all the numbers in a sequence, divided by the number of terms in that sequence.

Finding the First Arithmetic Mean:
Given, the two arithmetic means between -6 and 14. Let the first arithmetic mean be 'a'.
So, we can write the equation as:
-6, a, b, c, 14
where 'b' is the first arithmetic mean 'a' and 'c' is the second arithmetic mean.

We know that the formula to find the arithmetic mean is:
Mean = (Sum of all terms) / (Number of terms)
Using this formula, we can write the equation as:
a = (-6 + b + c + 14) / 4

Finding the Second Arithmetic Mean:
Now, we need to find the second arithmetic mean, which is 'c'.
We know that the sum of all the terms in the sequence is:
-6 + 14 + a + b + c
= 8 + a + b + c
Also, we know that the sum of all the terms in the sequence is:
= (Number of terms) * (Arithmetic Mean)
= 5 * ((-6 + c) / 2)
= (-15 + 5c) / 2

Equating both the equations, we get:
8 + a + b + c = (-15 + 5c) / 2
16 + 2a + 2b + 2c = -15 + 5c
2a + 2b + 3c = -31

Now, substituting the value of 'a' from the first equation we get:
2b + 3c = -19

Again, substituting the value of 'b' from the equation -6, a, b, c, 14, we get:
2a + 7c = 8

Solving these two equations, we get:
a = 5
b = -3
c = 1

Therefore, the two arithmetic means between -6 and 14 are -3 and 1.

1st A.M. = -6 + 20/3 = 2/3
2nd A.M. = 2/3 + 20/3 = 22/3