The problem asks to expand and simplify the expression $(2a+3)(3a-4)$.

1. Problem Description

The problem asks to expand and simplify the expression $(2a+3)(3a-4)$.

2. Solution Steps

To expand the expression $(2a+3)(3a-4)$, we use the distributive property (also known as the FOIL method):

$(A+B)(C+D) = AC + AD + BC + BD$

In this case, $A = 2a$, $B = 3$, $C = 3a$, and $D = -4$. Therefore:

$(2a+3)(3a-4) = (2a)(3a) + (2a)(-4) + (3)(3a) + (3)(-4)$

$(2a+3)(3a-4) = 6a^2 - 8a + 9a - 12$

Now, we combine the like terms:

$-8a + 9a = a$

So, the simplified expression is:

$6a^2 + a - 12$

3. Final Answer

$6a^2 + a - 12$