Veronica rolls a pair of dice twice. On both rolls, the sum is 9. Are these independent events, dependent events, or neither? Explain your answer.

The first roll has no effect what so ever on the results of the second roll. They are independent events.

Dependent events are those where the first outcome has an effect on the second. For example if you have two green balls and two red balls in a hat.
The probability of drawing a green one first is 2/4 or 1/2
However now you have a very different situation for your second draw due to the outcome of the first draw. You now have three of which one is green and two are red. The probability of drawing another green now is 1/3.
Therefore the probability of drawing both greens is
1/2 * 1/3 = 1/6
whereas if you had put that first green one back in the hat, then it would have been
1/2 * 1/2 = 1/4