This is one of the descriptions I've seen online:
For any even $n$, say $n = 2m$, a row complete Latin square of order $n$ can be formed by writing down
$$0, 1, 2m - 1, 2, 2m - 2, 3,\ldots, m + 1, m$$
as the first row and then developing subsequent rows by adding $1$ modulo $n$.
I'm not quite clear on how that goes, such as what the difference is between $2m$ and $m$. $2m$ stands for $n$, does $m$ stand for modulo? I'd like to see and example with an even number or two, such as $4$, and $6$.
I tried, $2m = 4$
$$0, 1, 3, 2, 2\ldots$$ wait, that can't be right.
It should turn out with non repeating sequences, and non recurring pairs between rows. I can outline the other methods I've found (but don't understand) if this one is not the best.