The word with the 3rd, 4th, 6th, and 7th letters being the same is "bookkeeper."
attach, attack
letters
SASSY or SORRY
plaza
pee
For a six-letter word to be a palindrome, the 3rd and 4th letters would have to be the same.
buzzingfizzing
juggler
wobbling
normally the 3rd or 4th letter
vinyl
Ferret.