To find the slope of the graph of $y = f(x)$ at the point $(2, 6)$, we need to calculate the derivative of $f(x)$ and evaluate it at $x = 2$.

Given the function:

$f(x) = 3x^2 - 5x + 4$

1. Find the derivative $f'(x)$:

   Differentiate the function with respect to $x$:

   $f'(x) = \frac{d}{dx} (3x^2) - \frac{d}{dx} (5x) + \frac{d}{dx} (4)$

   Simplifying this, we get:

   $f'(x) = 6x - 5$

2. Evaluate the derivative at $x = 2$:

   Substitute $x = 2$ into the derivative:

   $f'(2) = 6(2) - 5$

   $f'(2) = 12 - 5$

   $f'(2) = 7$

Therefore, the slope of the graph of $y = f(x)$ at the point $(2, 6)$ is 7.

Would you like more details on this solution, or do you have any questions? Here are some related questions that might interest you:

1. How do you find the slope of a curve at any given point?
2. What does the derivative of a function represent geometrically?
3. How can you verify that a point lies on a given curve?
4. What is the significance of a positive slope in a function's graph?
5. How do you find the equation of the tangent line to a curve at a given point?

Tip: The slope of the tangent line at a point on a curve gives the instantaneous rate of change of the function at that specific point.