AMC 10 2021-fall-b Problem 14

Una rolls $6$ standard $6$-sided dice simultaneously and calculates the product of the $6{ }$ numbers obtained. What is the probability that the product is divisible by $4?$ $\textbf{(A)}\: \frac34 \textbf{(B)} \: \frac{57}{64} \textbf{(C)} \: \frac{59}{64} \textbf{(D)} \: \frac{187}{192} \textbf{(E)} \: \frac{63}{64}$