We are asked to simplify the expression $2\sqrt{7} - \frac{14}{\sqrt{7}} + \frac{7}{\sqrt{21}}$.

1. Problem Description

We are asked to simplify the expression $2\sqrt{7} - \frac{14}{\sqrt{7}} + \frac{7}{\sqrt{21}}$.

2. Solution Steps

First, let's simplify the term $\frac{14}{\sqrt{7}}$.

We can rationalize the denominator by multiplying the numerator and denominator by $\sqrt{7}$:

$\frac{14}{\sqrt{7}} = \frac{14\sqrt{7}}{\sqrt{7}\sqrt{7}} = \frac{14\sqrt{7}}{7} = 2\sqrt{7}$.

Now, let's simplify the term $\frac{7}{\sqrt{21}}$.

We can rationalize the denominator by multiplying the numerator and denominator by $\sqrt{21}$:

$\frac{7}{\sqrt{21}} = \frac{7\sqrt{21}}{\sqrt{21}\sqrt{21}} = \frac{7\sqrt{21}}{21} = \frac{\sqrt{21}}{3}$.

So the expression becomes:

$2\sqrt{7} - 2\sqrt{7} + \frac{\sqrt{21}}{3} = 0 + \frac{\sqrt{21}}{3} = \frac{\sqrt{21}}{3}$.

3. Final Answer

The simplified expression is $\frac{\sqrt{21}}{3}$.

The answer is C.