Answer:

To divide the polynomial 6x^3 - 7x^2 - 16x^2 + 12 by 2x + 3, you can use long division. Here's how you can do it:

```

3x^2 - 2x + 4

______________________

2x + 3 | 6x^3 - 7x^2 - 16x^2 + 12

- (6x^3 + 9x^2)

______________________

-16x^2 + 12

- (-16x^2 - 24x)

______________________

36x + 12

- (36x + 54)

______________________

-42

```

So, when you divide 6x^3 - 7x^2 - 16x^2 + 12 by 2x + 3, the quotient is 3x^2 - 2x + 4, and the remainder is -42.