I am reading the proof of the divisibility rule for $7$ here (Aops page),but I can't see how $k-2n_0 \equiv 2n_0 +6k $ is derived.
I've tried to derive it by this: $$2n_0 +6k \equiv 2n_o +7k-k \equiv 2n_0-k, $$ but how can I get from this to $2n_0+6k \equiv k-2n_0$?