To solve the expression $(2x - 3)(3x - 4)$, we'll need to expand the product using the distributive property (also known as FOIL for binomials). Here's the step-by-step process:

Step 1: Use FOIL (First, Outer, Inner, Last)

• First: Multiply the first terms in each binomial:
  $2x \cdot 3x = 6x^2$

• Outer: Multiply the outer terms:
  $2x \cdot -4 = -8x$

• Inner: Multiply the inner terms:
  $-3 \cdot 3x = -9x$

• Last: Multiply the last terms in each binomial:
  $-3 \cdot -4 = 12$

Step 2: Combine like terms

Now, add all the terms together: $6x^2 - 8x - 9x + 12$

Combine the $x$-terms: $6x^2 - 17x + 12$

Final answer:

The expanded expression is $6x^2 - 17x + 12$.

Looking at the options, the correct choice is: $\boxed{6x^2 - 17x + 12}$

Would you like further details or explanations on any of the steps?

Here are 5 related questions:

1. How would you expand a binomial of the form $(ax + b)(cx + d)$?
2. Can you apply the distributive property to multiply three binomials?
3. What are the common mistakes made when using FOIL?
4. How do you factor a quadratic expression like $6x^2 - 17x + 12$?
5. How would the expression change if the signs inside the binomials were different?

Tip: Always be careful with the signs when using FOIL; combining like terms properly can help avoid errors.