2022 AMC 12B Problem 12

Kayla rolls four fair 6-sided dice. What is the probability that at least one of the numbers Kayla rolls is greater than 4 and at least two of the numbers she rolls are greater than 2?

\textbf{(A) }\frac{2}{3} \qquad \textbf{(B) }\frac{19}{27} \qquad \textbf{(C) }\frac{59}{81} \qquad \textbf{(D) }\frac{61}{81} \qquad \textbf{(E) }\frac{7}{9}

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