AMC 12 2022b 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 $2$?

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