Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x?

First, take a look at 3 less than twice x. Twice x would be 2x and 3 less than it would become 2x-3. 

Next, 2 more than the quantity 3 times x. The quantity of 3 times x is 3x and 2 more than that would be 3x+2. 

Now that we have our two equations, we need to multiply them together, which can be shown as (2x-3)(3x+2).

Then, multiply the two equations together using FOIL (multiply the first two terms, then the outside terms, then inside, and lastly, the last two terms): 2x times 3x, 2x times 2, -3x times 3x, and 2 times -3, which equates to 6x^2+4x-9x-6. 

Your final answer is 6x^2-5x-6.