Cayley Mathematical Olympiad 2020 Q6

Martha and Nadia play a game. Each has to make her own four-digit number, choosing her four digits from eight “digit cards” labelled 1-8.

First Martha chooses her thousands digit, and then Nadia chooses her thousands digit.Next, Martha chooses her hundreds digit from the remaining six cards, and then Nadia chooses her hundreds digit.This process is repeated for the tens and finally the units digits of their numbers. The two four-digit numbers produced are then added together.

Martha wins if the sum is not a multiple of 6; Nadia wins if the sum is a multiple of 6.

By showing that the final sum is always a multiple of $k$, it can be shown that Nadia can follow a strategy so that she always wins no matter which digits Martha chooses. find the value of $k$.