Here is the text of 2 John 6 according to the BLB:
And this is love, that we should walk according to His
commandments. This is the commandment, just as you have heard from the
beginning, so that you should walk in it.
I assume that the two instances of the verb περιπατέω (walk) are translated with and without the "should" is for a variety of reasons including:
- a matter of style to prevent verbal repetition
- to maintain some continuity with the KJV which did the same
- some things else, etc
I note that the YLT is similar to BSB and gives:
and this is the love, that we may walk according to His commands;
this is the command, even as ye did hear from the beginning, that in
it ye may walk,
Both cases of the verb are present subjunctive active - extremely difficult to convey accurately and unambiguously in English without appearing to give the wrong impression of simply giving permission rather than facilitating!
APPENDIX - Hebrew Parallelism
I cannot resist the obvious parallelism of the original text of 2 John 6 which is striking in the Greek so let me attempt to convey it thus (my translation):
And this is love:
- that we should walk according to His commandments
This is the commandment (just as you heard from the beginning)
- that in it you should walk