The given equation is $y = f(x) = -4x + 6$, which is in the form of a linear equation $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

In this case, the slope $m$ is the coefficient of $x$, which is -4.

So, the slope of the function $f(x) = -4x + 6$ is -4.

Would you like further clarification on slopes, or do you have any questions related to this?

Further questions:

1. How do you find the slope from a graph?
2. What does a negative slope represent in a real-world context?
3. How can you find the equation of a line if you're given the slope and a point on the line?
4. What is the significance of the y-intercept in a linear equation?
5. How does the slope change if the coefficient of $x$ increases or decreases?

Tip: If you have two points on a line, you can calculate the slope using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.