I’ve said this before but as much as I respect dealers as a group they give out a lot of bad advice and misinformation. Splitting fours against a five or six is a frequent play where both players and dealers incorrectly rebuke splitting. Sometimes you hear people say falsely that you should never split "anything that starts with F", in other words fours, fives, and faces. That is true about fives and faces but the player should indeed split fours against a five or six if double after split is allowed. Otherwise the player should hit, except in single deck he should double if allowed. My blackjack appendix 9 shows in a six-deck game where the dealer hits a soft 17 the following expected values of 4,4 against a 6.
Stand: -0.114085
Hit: + 0.113365
Double: + 0.092929
Split: +0.207228 (double after split allowed)
Split: + 0.056954 (double after split not allowed)