First teck connectors are required for wet locations or hazardous locations. Flex and BX connectors are approved for dry locations for teck assuming condition 1 and 2 do not exist. The biggest challenge with many of the dry connectors is that they do not tighten up to the armour thus neither a good mechanical or electrical connection.
Now #4 to #6. as long as the wire is that size for voltage drop and the OC protection is for #6 then great. Maybe the largest lugs in the supply and load would not accomodate #4 wires. I saw a job that sized all the home runs for %3 volt drop and a few receptacle runs used #6 which were spliced down to #12 for connection to breakers and receptacles. I think that job was designed by some guy that just took a harmonics and volt drop seminar. They might even recoup the added expense over a hundred years on line loss savings ;-) By the way it was an OSH (Worksafe) office in Vicoria BC.
