2022 AMC 8 Problem 17

If n is an even positive integer, the \textit{double factorial} notation n!! represents the product of all the even integers from 2 to n. For example, 8!! = 2 \cdot 4 \cdot 6 \cdot 8. What is the units digit of the following sum? 2!! + 4!! + 6!! + \cdots + 2018!! + 2020!! + 2022!!

\textbf{(A)} ~0\qquad\textbf{(B)} ~2\qquad\textbf{(C)} ~4\qquad\textbf{(D)} ~6\qquad\textbf{(E)} ~8

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