Step 1: Implicit differentiation
Differentiate $3y^2 - 2xy - x = 0$ with respect to $x$: $6y\,y' - 2y - 2x\,y' - 1 = 0$.
Step 2: Solve for y'
$y'(6y - 2x) = 2y + 1$, so $y' = \dfrac{2y + 1}{6y - 2x}$.
Step 3: Find x at y = 2
$12 - 4x - x = 0$ gives $x = \frac{12}{5}$.
Step 4: Evaluate
$y' = \dfrac{5}{12 - \frac{24}{5}} = \dfrac{5}{\frac{36}{5}} = \dfrac{25}{36}$.
Final Answer:
The derivative is 25/36. This is option (C).
\[ \boxed{\text{(C) }\frac{25}{36}} \]