To solve for $f(4)$ given the function $f(x) = 2x^2 - 3x$, we substitute $x = 4$ into the equation:

$f(4) = 2(4)^2 - 3(4)$

Let's calculate it step by step:

$f(4) = 2(16) - 12$ $f(4) = 32 - 12$ $f(4) = 20$

So, the correct value of $f(4)$ is 20, which corresponds to option A.

Would you like further explanation or have any questions? Here are some related questions:

1. How would the function change if we added a constant term?
2. What is the vertex of the quadratic function $f(x) = 2x^2 - 3x$?
3. How does the function behave for negative values of $x$?
4. Can you solve for $f(x) = 0$ to find the roots of the function?
5. What is the derivative of $f(x) = 2x^2 - 3x$?

Tip: When evaluating functions, always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).