Consider the equation $$x^2 + 4x - n = 0$$, where $$n \in [20, 100]$$ is a natural number. Then the number of all distinct values of n, for which the given equation has integral roots, is equal to

Let $$\alpha$$ and $$\beta$$ be the roots of the equation.

$$\Rightarrow$$ $$\alpha + \beta = -4$$ and $$\alpha\beta = -n$$

The roots of the equation should be integral.

We want pairs such that the sum of the roots is $$-4$$ and the product of the roots is $$-n$$, where $$n$$ lies in $$[20, 100]$$. Hence, the following possible pairs exist. We can enumerate the cases and find out the number of distinct values of $$n$$

$$(3, -7) \Rightarrow n = 21$$

$$(4, -8) \Rightarrow n = 32$$

$$(5, -9) \Rightarrow n = 45$$

$$(6, -10) \Rightarrow n = 60$$

$$(7, -11) \Rightarrow n = 77$$

$$(8, -12) \Rightarrow n = 96$$

This gives 6 possible values of $$n$$

Thus, option C is the correct choice.