2024 AMC 8 Problem 5

Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of 6. Which of the following integers cannot be the sum of the two numbers?

\textbf{(A)} 5 \qquad \textbf{(B)} 6 \qquad \textbf{(C)} 7 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.