We substitute the given values into the formula:
$\text{J}(2, 12, 9) = \frac{2}{12} + \frac{12}{9} + \frac{9}{2}$.
We simplify each fraction:
$\frac{2}{12} = \frac{1}{6}$,
$\frac{12}{9} = \frac{4}{3}$,
$\frac{9}{2} = \frac{9}{2}$.
We add the fractions:
$\frac{1}{6} + \frac{4}{3} + \frac{9}{2}$.
We find a common denominator:
$\frac{1}{6} + \frac{8}{6} + \frac{27}{6}$.
We add the numerators and keep the denominator:
$\frac{1+8+27}{6} = \frac{36}{6}$.
We simplify the fraction:
$\frac{36}{6} = \boxed{6}$.
The answer is: 6
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Calculate the value of $\text{J}(2, 12, 9)$, where $\text{J}(a, b, c) = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ for nonzero values of $a$, $b$, and $c$.

### Answer:
