Hi there! Thank you for the opportunity to help you with your question!

For solving this problem, we first need to simplify the quantities inside the parentheses. That is:

6x²((3x-4)+(4x+2))

=6x²(7x-2) [where we combined the like terms 3x+4x = 7x, and -4 + 2 =-2

Now we use the distributive property. The distributive property says that when you are multiplying an expression of the form a*(b + c), that you "distribute" the outside term a into both terms inside parentheses, that is a*b + a*c. In this case, the expression becomes:

=6x² * 7x + 6x² *(-2) = 42x^3-12x²

Please let me know if you need any clarification. Always glad to help!